T-S模糊系统的若干控制问题研究
|
摘要
随着科学的日益发展,我们对控制系统的要求越来越高,系统也日趋复杂,并且由于被控对象或过程的非线性、较大的随机干扰、各种不确定性等因素的影响经常导致难以建立满足控制要求的数学模型。对于这样的系统,传统的控制理论则很难被应用。而模糊控制技术由于其自身具有人类自然语言的定性描述的特点,能够有效地克服这些困难实现对被控对象的控制。特别地,基于T-S模糊模型的非线性系统的稳定性分析和控制器设计的研究近年来吸引了广大学者和专家的兴趣。许多重要的进步已经被取得。但是由于模糊控制系统固有的非线性特性,探求更加有效的模糊系统的稳定性分析和控制器设计条件仍然是模糊控制理论研究的一项重要的任务。
本论文在总结前人工作的基础上,进一步深入地研究了T-S模糊系统的若干控制问题。具体如下：针对连续T-S模糊系统,使用模糊隶属度函数的性质,提出了新的线性矩阵不等式(LMI)技术,它能引入比已有方法更多的LMI变量,进而获得了具有更少保守性的稳定性分析和控制器设计条件；针对离散T-S模糊系统，通过使用输出矩阵核空间的性质,给出了新的基于LMI的方法来设计H∞静态输出反馈控制器,并出示了所提出方法能给出比已有方法更少保守性的解；首次提出了T-S模糊系统的一类新的控制策略,即,切换PDC控制策略,并给出了基于LMI的切换PDC控制器设计方法,减少了目前控制器设计方法的保守性；针对已有复杂的非线性系统的T-S模糊模型具有太多模糊规则导致控制器难以设计和实施的困难,给出了一类由局部非线性子模型构成的T-S模糊模型的建模方法及相应的控制器设计技术。所提出的方法能减少传统方法的计算负担并构造出具有更少模糊规则的控制器,而且它也可以给出更少保守性的解；针对模糊奇异摄动系统,提出一类能够改善奇异摄动参数的上界新的控制器设计技术,进而克服了已有奇异摄动系统控制器设计技术无法改善奇异摄动参数的上界的缺点；此外,针对模糊马尔可夫跳变系统,给出了新的基于LMI的模型独立控制器的设计条件,新的条件中引入了比已有方法更多的LMI变量,于是增加了算法的自由度,进而能够给出更少保守性的解。
本文的主要研究内容如下：
第一章系统地分析和总结了模糊控制理论研究领域的发展现状。
第二章针对连续T-S模糊系统,使用模糊Lyapunov函数,通过探求一个可以引入更多的变量新的LMI技术获得了一个带有线性搜索的基于LMI的控制器设计方法。与已有的方法相比,更多的松弛变量增加了算法的自由度,于是可以得到更少保守性的解。进一步通过数值例子验证了该方法的有效性。针对离散T-S模糊系统,首次利用系统输出矩阵的核空间的性质引入带有下三角结构的参数依赖的松弛变量,给出了基于LMI的静态输出反馈控制器设计条件。与已有的静态输出反馈控制器设计技术相比,所提出的方法避免了对Lyapunov矩阵的约束,可以给出更少保守性的设计。仿真算例出示了所提出方法的有效性。
第三章通过深入分析模糊系统的特点,首次提出了一类依赖于模糊隶属度函数值进行切换的控制策略,即,切换PDC控制策略。本章分别给出了连续和离散T-S模糊系统的基于LMI的切换PDC控制器设计方法。所提出的方法包含了已有的PDC控制器设计方法和切换线性控制器设计方法,因此它能给出更少保守性的结果。仿真算例进一步表明本章所提出方法相对于已有方法的优越性。
第四章考虑了复杂非线性系统的模糊控制器设计问题。这样的系统的T-S模糊模型通常有大量模糊规则,于是基于这个模糊模型的控制器设计方法经常有非常大的计算负担以至于可能无法得到可行的结果,即使能得到可行的结果,但因为所设计的控制器具有大量的模糊规则而不便于工程实施。为了克服这一困难,本章首次提出带有局部非线性子模型的T-S模糊模型的建模技术并给出了相应的控制器设计方法。与已有的方法相比,新的方法能获得更少模糊规则的控制器并且有更少的计算负担。特别地,非线性子模型的使用可以保留非线性系统重要的非线性属性,于是它也能够给出更少保守性的解。仿真算例进一步验证了所提出方法的有效性。
第五章考虑了奇异摄动T-S模糊系统的控制器设计和奇异参数摄动界的估计问题。针对连续奇异摄动T-S模糊系统,首次给出了能够通过设计控制器来改善奇异摄动参数上界的控制器设计技术。针对离散奇异摄动系统提出了两个仅使用慢状态信息的H∞控制器设计的LMI条件,其中之一可以通过设计控制器来改善奇异摄动参数上界。特别地,这两个条件都移除了已有的基于Riccati方程或不等式方法只能应用于满足正则性的系统的约束。仿真算例进一步表明所提出优化方法的有效性。
第六章针对连续马尔可夫跳变系统,使用随机Lyapunov函数方法并通过新的LMI技术引入了松弛变量分离系统矩阵和随机Lyapunov矩阵,给出了基于LMI的模型独立的控制器设计条件。与已有的方法相比,所提出的方法引入了更多的LMI变量,进而能给出更少保守性的解。这一事实将通过理论证明和仿真算例进一步验证。
最后对全文所做的工作进行了总结,并指明了下一步研究的方向。
With the developments of the science, we have more requirements for control sys-tems and the control systems are more complex. The controlled object or process often is nonlinear, subject to some random disturbances and uncertainties, so that its mathe-matical model, which can satisfy our demands, is not available. For the control system, the conventional control theory is not applicable. However, the fuzzy control techniques with a property of human language can overcome the difficulties. In particular, stability analysis and control synthesis of nonlinear systems described by T-S fuzzy models appeal many researchers'interest and many important progresses have been achieved. Due to the inherent nonlinearities of T-S fuzzy systems, it is still a very important task to exploit more effective conditions for stability analysis and control synthesis.
Based on the previous work of other researchers, this thesis further studies some control problems of T-S fuzzy systems, which are given as follows:By using the prop-erties of fuzzy membership functions, a new LMI technique, which can introduce more LMI variables than the existing ones, is proposed. Further, by the new technique, the conditions with less conservatism are given for stability analysis and control synthesis for continuous-time T-S fuzzy systems; By using the properties of the null space of sys-tem output matrix, a new LMI-based condition for designing H^ static output feedback controllers for discrete-time T-S fuzzy systems is given. In contrast to the existing ap-proaches, the new one removes the constraint on the structure of Lyapunov matrices, then it can gives less conservative results; A new control scheme for T-S fuzzy systems, i.e., switching PDC control scheme, is proposed for the first time. The corresponding LMI-based control design approaches are given. The proposed approaches can be reduced to the PDC controller design methods or switching linear controller design methods under some additional constraints, then they can give less conservative results; A new type of T-S fuzzy models, which consist of local nonlinear subsystems, is constructed for a class of nonlinear systems with strong nonlinearities, and the corresponding conditions for design-ing controllers are given. The proposed approach can overcome the difficulty of designing controllers based on the conventional T-S fuzzy models due to too many fuzzy rules in the model. It can reduce the computational burden and give less conservative results; A controller design method for singularly perturbed fuzzy systems, which can improve the upper bound of the singular perturbation parameter by designing controllers, is given. The proposed method overcomes the difficulty that the existing approaches cannot improve the upper bound of the singular perturbation parameter by designing controllers. Moreover, a new condition for designing mode-independent controllers for Markovian jump fuzzy systems is given. More slack variables are introduced in the proposed condition, then the proposed method is more flexible in the freedom and can given less conservative results than the existing ones.
The considered main issues are given as follows:
In Chapter 1, the background and the development of fuzzy control are summarized and analyzed.
In Chapter 2, a new LMI technique, which can introduce more variables, is ex-ploited, then an LMI-based method with a linear search for designing fuzzy controllers for continuous-time T-S fuzzy systems is obtained. In contrast to the existing approaches, the new one is more flexible in the freedom due to more slack variables, therefore, it can give less conservative results. Numerical examples are further given for showing the effectiveness of the proposed approach. Moreover, by using the properties of the null space of output matrices, a parameter-dependent slack variable with lower-triangular structure is introduced, then a new method for designing static output feedback controllers is obtained. In contrast to the existing approaches, the proposed method can remove the constraint on Lyapunov matrices and give less conservative results. Numerical examples validate the effectiveness of the proposed approach
In Chapter 3. by analyzing the properties of fuzzy systems, a new control scheme, i.e., switching PDC control scheme, is proposed for the first time. LMI-based condi-tions for designing switching PDC controllers are given respectively for continuous and discrete-time T-S fuzzy systems. The existing PDC controller design methods or switch-ing linear controller design methods can be considered as a special case of the new control scheme. Therefore, the proposed method can give less conservative results than the ex-isting ones. Numerical examples are given to show the effectiveness of the proposed approaches.
In Chapter 4, fuzzy controller design problems of a class of nonlinear systems with complex nonlinearities are considered. The T-S fuzzy models of the class of nonlinear systems are of very many fuzzy rules, so that the methods for designing controller have heavy computational burden or cannot get a feasible solution. Moreover, the obtained controllers are not convenient for implementing in engineering. In order to overcome the difficulty, a new type of T-S fuzzy models with local nonlinear subsystems are proposed and the corresponding control synthesis techniques are given. In contrast to the existing approaches, the proposed one can obtain a fuzzy controller with less fuzzy rules and has less computational burden. In particular, some important properties of nonlinear systems can be reserved due to the use of the nonlinear subsystems, then it also can give less conservative results. The effectiveness of the proposed method is validated by numerical examples.
In Chapter 5, the problems of the controller design, and the estimation of the up-per bound of singular perturbation parameter of singularly perturbed fuzzy systems are considered. A controller design method with improving the upper bound of the singular perturbation parameter is given for the first time for continuous-time singularly perturbed fuzzy systems. Moreover, two LMI-based conditions for designing Hx controllers only by slow state information for discrete-time singularly perturbed fuzzy systems are pro-posed, where one of them can improve the upper of singular perturbation parameter by designing controllers. Both of them remove the constraint on Riccati equation or inequal-ity approaches, where the systems have to satisfy the regularity. The effectiveness of the proposed methods are validated by numerical examples.
In Chapter 6, based on stochastic Lyapunov functions and by introducing slack vari-ables for separating the system matrix and Lyapunov matrix, an LMI-based condition for designing mode-independent controllers is given for Markovian jump fuzzy systems. In contrast to the existing approach, the proposed method is of more LMI variables, then can give less conservative results. Numerical examples further show the effectiveness of the proposed method.
Finally, the results of the dissertation are summarized and further research topics are pointed out.
本论文在总结前人工作的基础上,进一步深入地研究了T-S模糊系统的若干控制问题。具体如下：针对连续T-S模糊系统,使用模糊隶属度函数的性质,提出了新的线性矩阵不等式(LMI)技术,它能引入比已有方法更多的LMI变量,进而获得了具有更少保守性的稳定性分析和控制器设计条件；针对离散T-S模糊系统，通过使用输出矩阵核空间的性质,给出了新的基于LMI的方法来设计H∞静态输出反馈控制器,并出示了所提出方法能给出比已有方法更少保守性的解；首次提出了T-S模糊系统的一类新的控制策略,即,切换PDC控制策略,并给出了基于LMI的切换PDC控制器设计方法,减少了目前控制器设计方法的保守性；针对已有复杂的非线性系统的T-S模糊模型具有太多模糊规则导致控制器难以设计和实施的困难,给出了一类由局部非线性子模型构成的T-S模糊模型的建模方法及相应的控制器设计技术。所提出的方法能减少传统方法的计算负担并构造出具有更少模糊规则的控制器,而且它也可以给出更少保守性的解；针对模糊奇异摄动系统,提出一类能够改善奇异摄动参数的上界新的控制器设计技术,进而克服了已有奇异摄动系统控制器设计技术无法改善奇异摄动参数的上界的缺点；此外,针对模糊马尔可夫跳变系统,给出了新的基于LMI的模型独立控制器的设计条件,新的条件中引入了比已有方法更多的LMI变量,于是增加了算法的自由度,进而能够给出更少保守性的解。
本文的主要研究内容如下：
第一章系统地分析和总结了模糊控制理论研究领域的发展现状。
第二章针对连续T-S模糊系统,使用模糊Lyapunov函数,通过探求一个可以引入更多的变量新的LMI技术获得了一个带有线性搜索的基于LMI的控制器设计方法。与已有的方法相比,更多的松弛变量增加了算法的自由度,于是可以得到更少保守性的解。进一步通过数值例子验证了该方法的有效性。针对离散T-S模糊系统,首次利用系统输出矩阵的核空间的性质引入带有下三角结构的参数依赖的松弛变量,给出了基于LMI的静态输出反馈控制器设计条件。与已有的静态输出反馈控制器设计技术相比,所提出的方法避免了对Lyapunov矩阵的约束,可以给出更少保守性的设计。仿真算例出示了所提出方法的有效性。
第三章通过深入分析模糊系统的特点,首次提出了一类依赖于模糊隶属度函数值进行切换的控制策略,即,切换PDC控制策略。本章分别给出了连续和离散T-S模糊系统的基于LMI的切换PDC控制器设计方法。所提出的方法包含了已有的PDC控制器设计方法和切换线性控制器设计方法,因此它能给出更少保守性的结果。仿真算例进一步表明本章所提出方法相对于已有方法的优越性。
第四章考虑了复杂非线性系统的模糊控制器设计问题。这样的系统的T-S模糊模型通常有大量模糊规则,于是基于这个模糊模型的控制器设计方法经常有非常大的计算负担以至于可能无法得到可行的结果,即使能得到可行的结果,但因为所设计的控制器具有大量的模糊规则而不便于工程实施。为了克服这一困难,本章首次提出带有局部非线性子模型的T-S模糊模型的建模技术并给出了相应的控制器设计方法。与已有的方法相比,新的方法能获得更少模糊规则的控制器并且有更少的计算负担。特别地,非线性子模型的使用可以保留非线性系统重要的非线性属性,于是它也能够给出更少保守性的解。仿真算例进一步验证了所提出方法的有效性。
第五章考虑了奇异摄动T-S模糊系统的控制器设计和奇异参数摄动界的估计问题。针对连续奇异摄动T-S模糊系统,首次给出了能够通过设计控制器来改善奇异摄动参数上界的控制器设计技术。针对离散奇异摄动系统提出了两个仅使用慢状态信息的H∞控制器设计的LMI条件,其中之一可以通过设计控制器来改善奇异摄动参数上界。特别地,这两个条件都移除了已有的基于Riccati方程或不等式方法只能应用于满足正则性的系统的约束。仿真算例进一步表明所提出优化方法的有效性。
第六章针对连续马尔可夫跳变系统,使用随机Lyapunov函数方法并通过新的LMI技术引入了松弛变量分离系统矩阵和随机Lyapunov矩阵,给出了基于LMI的模型独立的控制器设计条件。与已有的方法相比,所提出的方法引入了更多的LMI变量,进而能给出更少保守性的解。这一事实将通过理论证明和仿真算例进一步验证。
最后对全文所做的工作进行了总结,并指明了下一步研究的方向。
With the developments of the science, we have more requirements for control sys-tems and the control systems are more complex. The controlled object or process often is nonlinear, subject to some random disturbances and uncertainties, so that its mathe-matical model, which can satisfy our demands, is not available. For the control system, the conventional control theory is not applicable. However, the fuzzy control techniques with a property of human language can overcome the difficulties. In particular, stability analysis and control synthesis of nonlinear systems described by T-S fuzzy models appeal many researchers'interest and many important progresses have been achieved. Due to the inherent nonlinearities of T-S fuzzy systems, it is still a very important task to exploit more effective conditions for stability analysis and control synthesis.
Based on the previous work of other researchers, this thesis further studies some control problems of T-S fuzzy systems, which are given as follows:By using the prop-erties of fuzzy membership functions, a new LMI technique, which can introduce more LMI variables than the existing ones, is proposed. Further, by the new technique, the conditions with less conservatism are given for stability analysis and control synthesis for continuous-time T-S fuzzy systems; By using the properties of the null space of sys-tem output matrix, a new LMI-based condition for designing H^ static output feedback controllers for discrete-time T-S fuzzy systems is given. In contrast to the existing ap-proaches, the new one removes the constraint on the structure of Lyapunov matrices, then it can gives less conservative results; A new control scheme for T-S fuzzy systems, i.e., switching PDC control scheme, is proposed for the first time. The corresponding LMI-based control design approaches are given. The proposed approaches can be reduced to the PDC controller design methods or switching linear controller design methods under some additional constraints, then they can give less conservative results; A new type of T-S fuzzy models, which consist of local nonlinear subsystems, is constructed for a class of nonlinear systems with strong nonlinearities, and the corresponding conditions for design-ing controllers are given. The proposed approach can overcome the difficulty of designing controllers based on the conventional T-S fuzzy models due to too many fuzzy rules in the model. It can reduce the computational burden and give less conservative results; A controller design method for singularly perturbed fuzzy systems, which can improve the upper bound of the singular perturbation parameter by designing controllers, is given. The proposed method overcomes the difficulty that the existing approaches cannot improve the upper bound of the singular perturbation parameter by designing controllers. Moreover, a new condition for designing mode-independent controllers for Markovian jump fuzzy systems is given. More slack variables are introduced in the proposed condition, then the proposed method is more flexible in the freedom and can given less conservative results than the existing ones.
The considered main issues are given as follows:
In Chapter 1, the background and the development of fuzzy control are summarized and analyzed.
In Chapter 2, a new LMI technique, which can introduce more variables, is ex-ploited, then an LMI-based method with a linear search for designing fuzzy controllers for continuous-time T-S fuzzy systems is obtained. In contrast to the existing approaches, the new one is more flexible in the freedom due to more slack variables, therefore, it can give less conservative results. Numerical examples are further given for showing the effectiveness of the proposed approach. Moreover, by using the properties of the null space of output matrices, a parameter-dependent slack variable with lower-triangular structure is introduced, then a new method for designing static output feedback controllers is obtained. In contrast to the existing approaches, the proposed method can remove the constraint on Lyapunov matrices and give less conservative results. Numerical examples validate the effectiveness of the proposed approach
In Chapter 3. by analyzing the properties of fuzzy systems, a new control scheme, i.e., switching PDC control scheme, is proposed for the first time. LMI-based condi-tions for designing switching PDC controllers are given respectively for continuous and discrete-time T-S fuzzy systems. The existing PDC controller design methods or switch-ing linear controller design methods can be considered as a special case of the new control scheme. Therefore, the proposed method can give less conservative results than the ex-isting ones. Numerical examples are given to show the effectiveness of the proposed approaches.
In Chapter 4, fuzzy controller design problems of a class of nonlinear systems with complex nonlinearities are considered. The T-S fuzzy models of the class of nonlinear systems are of very many fuzzy rules, so that the methods for designing controller have heavy computational burden or cannot get a feasible solution. Moreover, the obtained controllers are not convenient for implementing in engineering. In order to overcome the difficulty, a new type of T-S fuzzy models with local nonlinear subsystems are proposed and the corresponding control synthesis techniques are given. In contrast to the existing approaches, the proposed one can obtain a fuzzy controller with less fuzzy rules and has less computational burden. In particular, some important properties of nonlinear systems can be reserved due to the use of the nonlinear subsystems, then it also can give less conservative results. The effectiveness of the proposed method is validated by numerical examples.
In Chapter 5, the problems of the controller design, and the estimation of the up-per bound of singular perturbation parameter of singularly perturbed fuzzy systems are considered. A controller design method with improving the upper bound of the singular perturbation parameter is given for the first time for continuous-time singularly perturbed fuzzy systems. Moreover, two LMI-based conditions for designing Hx controllers only by slow state information for discrete-time singularly perturbed fuzzy systems are pro-posed, where one of them can improve the upper of singular perturbation parameter by designing controllers. Both of them remove the constraint on Riccati equation or inequal-ity approaches, where the systems have to satisfy the regularity. The effectiveness of the proposed methods are validated by numerical examples.
In Chapter 6, based on stochastic Lyapunov functions and by introducing slack vari-ables for separating the system matrix and Lyapunov matrix, an LMI-based condition for designing mode-independent controllers is given for Markovian jump fuzzy systems. In contrast to the existing approach, the proposed method is of more LMI variables, then can give less conservative results. Numerical examples further show the effectiveness of the proposed method.
Finally, the results of the dissertation are summarized and further research topics are pointed out.
引文
1. Zadeh L A. Fuzzy sets[J], Information and Control,1965.8(3):338-353.
2.张天平.基于一种修改的李亚普诺夫函数的自适应模糊滑模控制[Jl,自动化学报，2002,28(1)：137-142.
3.应浩.关于模糊控制理论与应用的若干问题[J],自动化学报,2001,27(4)：591-592.
4.孙增圻.基于模糊状态模型的连续系统控制器设计和稳定性分析[J],自动化学报.1998,24(2)：212-216.
5.张松涛,任光.基于分段模糊Lyapunov方法的离散模糊系统分析与设计[J],自动化学报.2006,32(5)：813-818.
6.刘亚,胡寿松.不确定非线性系统的模糊鲁棒跟踪控制[J],自动化学报,2004,30(6)：949-953.
7.修智宏,任光.T-S模糊控制系统的稳定性分析及系统化设计[J],自动化学报,2004,30(5)：731-740.
8.胡包钢,应浩.模糊PID控制技术研究发展回顾及其面临的若干重要问题[J]，Acta Automatica Sinica,2001,27(4):567-584.
9.邱焕耀,毛宗源.采用模糊控制的感应电动机解耦变结构系统的研究[Jl,自动化学报，1998,24(3)：391-394.
10.姚尹武，熊金涛.一种神经网络自组织模糊控制[J],控制理论与应用,1996,13(6)：738-744.
11.张金明,李人厚.模糊控制的系统化设计和稳定性分析[J]，自动化学报,1999,25(4)：493-497.
12.丁海山,毛剑琴,林岩.基于模糊树模型的自适应直接逆控制[J],自动化学报,2008,34(5)：574-580.
13.罗艳斌,曹永岩，孙优贤.具有时变输入时滞的不确定TS模糊系统的鲁棒稳定性[J],自动化学报,2008,87-92：1.
14.巩长忠.王伟,刘全利.基于观测器的非线性不确定离散系统的鲁棒模糊控制[J],控制理论与应用,2005,22(1)：96-100.
15.丁宝苍，孙鹤旭,乔玉娥.基于参数Lyapunov函数的T-S模糊控制系统的稳定性分析[J],自动化学报,2005,31(4)：651-654.
16.李祖欣,王万良，雷必成,陈惠英.网络控制系统中基于模糊反馈的消息调度[J],自动化学报,2007，33(11)：1229-1232.
17.刘华平,孙富春，孙增圻.李春文.基于部分状态信息的模糊控制器设计[J],自动化学报,2004,30(6)：999-1003.
18.张化光.王智良,黎明,全永兵，张明君.广义模糊双曲正切模型：一个万能逼近器[J],自动化学报,2004,30(3)：416-422.
19.张大庆,张庆灵,胡跃冰.TS模糊系统稳定性的一个新的充分条件[J],自动化学报,2007,33(2)：222-224.
20. Takagi T. Sugeno M. Fuzzy identification of systems and its applications to mod-eling and control[J], IEEE Transactions on Systems, Man and Cybernetics,1985, SMC-15(1):116-132.
21. Cao S G, Rees N W, Feng G. Analysis and design for a class of complex control sys-tems Part Ⅰ:Fuzzy modelling and identification[J], Automatica,1997,33(6):1017-1028.
22. Johansen T A, Shorten R, Murray-Smith R. On the interpretation and identification of dynamic Takagi-Sugeno fuzzy models[J], IEEE Transactions on Fuzzy Systems, 2000,8(3):297-313.
23. Tanaka K, Wang H O. Fuzzy Control Systems Design and Analysis:A Linear Matrix Inequality Approach[M], New York, NY, USA:John Wiley & Sons, Inc., 2001.
24. Ying H. General SISO Takagi-Sugeno fuzzy systems with linear rule consequent are universal approximators[J]. IEEE Transactions on Fuzzy Systems,1998,6(4):582-587.
25. Zeng K. Zhang N Y, Xu W L. A comparative study on sufficient conditions for Takagi-Sugeno fuzzy systems as universal approximators[J], IEEE Transactions on Fuzzy Systems,2000,8(6):773-780.
26. Feng G. A survey on analysis and design of model-based fuzzy control systems[J], IEEE Transactions on Fuzzy Systems.2006,14(5):676-697.
27. Sala A, Guerra T M, Babuska R. Perspectives of fuzzy systems and control[J], Fuzzy Sets and Systems,2005,156(3):432-444.
28. Fang C H, Liu Y S, Kau S W, et al. A new LMI-based approach to relaxed quadratic stabilization of T-S fuzzy control systems[J], IEEE Transactions on Fuzzy Systems. 2006,14(3):386-397.
29. Ho D W C, Niu Y. Robust fuzzy design for nonlinear uncertain stochastic systems via sliding-mode control[J], IEEE Transactions on Fuzzy Systems.2007,15(3):350-358.
30. Huang D, Nguang S K. Robust H∞ static output feedback control of fuzzy systems: an ILMI approach[J], IEEE Transactions on Systems, Man and Cybernetics, Part B, 2006,36(1):216-222.
31. Kim E, Lee H. New approaches to relaxed quadratic stability condition of fuzzy control systems[J], IEEE Transactions on Fuzzy Systems,2000,8(5):523-534.
32. Li T H S, Tsai S H. T-S fuzzy bilinear model and fuzzy controller design for a class of nonlinear systems[J], IEEE Transactions on Fuzzy Systems,2007,15(3):494-506.
33. Lian K Y, Liou J J. Output tracking control for fuzzy systems via output feedback design[J], IEEE Transactions on Fuzzy Systems,2006,14(5):628-639.
34. Liu X, Zhang Q. New approaches to H∞ controller designs based on fuzzy observers for T-S fuzzy systems via LMI[J], Automatica,2003,39(9):1571-1582.
35. Sala A, Arino C. Asymptotically necessary and sufficient conditions for stability and performance in fuzzy control:Applications of Polya's theorem[J], Fuzzy Sets and Systems,2007,158(24):2671-2686.
36. Tanaka K, Ikeda T, Wang H O. Fuzzy regulators and fuzzy observers:relaxed stability conditions and LMI-based designs[J], IEEE Transactions on Fuzzy Systems, 1998.6(2):250-265.
37. Teixeira M C M, Assuncao E. Avellar R G. On relaxed LMI-based designs for fuzzy regulators and fuzzy observers[J], IEEE Transactions on Fuzzy Systems,2003, 11(5):613-623.
38. Tuan H D. Apkarian P, Narikiyo T, et al. Parameterized linear matrix inequality techniques in fuzzy control system design[J], IEEE Transactions on Fuzzy Systems, 2001,9(2):324-332.
39. Tseng C S, Hwang C K. Fuzzy observer-based fuzzy control design for nonlin-ear systems with persistent bounded disturbances [J], Fuzzy Sets and Systems,2007, 158(2):164-179.
40. Tanaka K, Hori T, Wang H O. A multiple Lyapunov function approach to stabi-lization of fuzzy control systems[J], IEEE Transactions on Fuzzy Systems,2003, 11(4):582-589.
41. Wang W J, Chen Y J, Sun C H. Relaxed stabilization criteria for discrete-time T-S fuzzy control systems based on a switching fuzzy model and piecewise Lyapunov function[J], IEEE Transactions on Systems, Man and Cybernetics, Part B,2007, 37(3):551-559.
42. Wang W J, Sun C H. Relaxed stability and stabilization conditions for a T-S fuzzy discrete system[J], Fuzzy Sets and Systems.2005,156(2):208-225.
43. Guerra T M, Vermeiren L. LMI-based relaxed nonquadratic stabilization conditions for nonlinear systems in the Takagi-Sugeno's form[J], Automatica,2004,40(5):823-829.
44. Johansson M, Rantzer A, Arzen K E. Piecewise quadratic stability of fuzzy sys-tems[J], IEEE Transactions on Fuzzy Systems,1999,7(6):713-722.
45. Feng G. Controller synthesis of fuzzy dynamic systems based on piecewise Lya-punov functions[J], IEEE Transactions on Fuzzy Systems,2003,11(5):605-612.
46. Feng G. H∞ controller design of fuzzy dynamic systems based on piecewise Lya-punov functions[J], IEEE Transactions on Systems, Man and Cybernetics, Part B, 2004,34(1):283-292.
47. Feng G. Stability analysis of discrete-time fuzzy dynamic systems based on piece-wise Lyapunov functions[J], IEEE Transactions on Fuzzy Systems,2004,12(1):22-28.
48. Chen C L, Feng G, Sun D, et al. H∞ output feedback control of discrete-time fuzzy systems with application to chaos control[J], IEEE Transactions on Fuzzy Systems, 2005,13(4):531-543.
49. Kruszewski A, Wang R, Guerra T M. Nonquadratic stabilization conditions for a class of uncertain nonlinear discrete time TS fuzzy models:a new approach[J], IEEE Transactions on Automatic Control,2008,53(2):606-611.
50. Kokotovic P V, O'Reilly J, Khalil H K. Singular Perturbation Methods in Control: Analysis and Design[M], Orlando, FL, USA:Academic Press, Inc.,1986.
51. Dong J, Yang G H. H∞ control for fast sampling discrete-time singularly perturbed systems[J], Automatica,2008,44(5):1385-1393.
52. Dong J, Yang G H. Robust H∞ control for standard discrete-time singu-larly perturbed systems[J], IEE Proceedings-Control Theory & Applications,2007. 1(4):1141-1148.
53. Du Z. Singularly perturbed third-order boundary value problem for nonlinear sys-tems[J], Applied Mathematics and Computation,2007,189(1):869-877.
54. Li T H S, Lin K J. Composite fuzzy control of nonlinear singularly perturbed sys-tems[J], IEEE Transactions on Fuzzy Systems,2007.15(2):176-187.
55. Mukaidani H. A numerical algorithm for finding solution of sign-indefinite alge-braic Riccati equations for general multiparameter singularly perturbed systems[J], Applied Mathematics and Computation,2007,189(1):255-270.
56. Assawinchaichote W, Nguang S K. Fuzzy H∞ output feedback control design for singularly perturbed systems with pole placement constraints:an LMI approach[J], IEEE Transactions on Fuzzy Systems,2006,14(3):361-371.
57. Lin K J, Li T H S. Stabilization of uncertain singularly perturbed systems with pole-placement constraints[J], IEEE Transactions On Circuits And Systems II-Express Briefs.2006.53(9):916-920.
58. Lu G, Ho D W C. Generalized quadratic stability for continuous-time singular systems with nonlinear perturbation[J]. IEEE Transactions on Automatic Control, 2006,51 (5):818-823.
59. Nair J M, Lazar A, Bandyopadhyay B. Robust control for uncertain singularly perturbed systems using periodic output feedback[C], American Control Conference. Minneapolis, MN, United States:2006:4326-4331.
60. Shao Z H, Sawan M E. Stabilisation of uncertain singularly perturbed systems[J], IEE Proceedings-Control Theory and Applications,2006,153(1):99-103.
61. Son J W, Lim J T. Robust stability of nonlinear singularly perturbed system with un-certainties[J], IEE Proceedings-Control Theory and Applications,2006,153(1):104-110.
62. Choi H L, Shin Y S, Lim J T. Control of nonlinear singularly perturbed systems using feedback linearisation[J], IEE Proceedings-Control Theory and Applications, 2005,152(1):91-94.
63. Li T H S, Lin K J. Stabilization of singularly perturbed fuzzy systems[J], IEEE Transactions on Fuzzy Systems,2004,12(5):579-595.
64. Shao Z H. Robust stability of two-time-scale systems with nonlinear uncertain-ties[J], IEEE Transactions on Automatic Control.2004,49(2):258-261.
65. Hsiao F H, Hwang J D, Pan S T. D-stability problem of discrete singularly perturbed systems[J], International Journal of Systems Science,2003,34(3):227-236.
66. Datta K B, RaiChaudhuri A. H2/H∞ control of discrete singularly perturbed sys-tems:the state feedback case[J], Automatica,2002,38(10):1791-1797.
67. Kim B S, Kim Y J. Lim M T. LQG control for nonstandard singularly perturbed discrete time systems[C], Proc.41st IEEE Conf. Decision and Control. Las Vegas, Nevada USA,2002.4:3736-3741.
68. Lim M T, Kang C G, Kim B S. Optimal control of linear nonstandard singu-larly perturbed discrete systems[J], Dynamics of Continuous Discrete and Impulsive Systems-Series B-Applications & Algorithms,2002,9(2):163-174.
69. Fridman E. Near-optimal H∞ control of linear singularly perturbed systems[J], IEEE Transactions on Automatic Control,1996,41 (2):236-240.
70. Gajic Z, Koskie S, Coumarbatch C. On the singularly perturbed matrix differ-ential Riccati equation[C], The 44th IEEE Conference on Decision and Control. 2005:3638-3644.
71. Guan Z H, Hill D J, Shen X. On hybrid impulsive and switching systems and ap-plication to nonlinear control[J], IEEE Transactions on Automatic Control,2005, 50(7):1058-1062.
72. Han H, Morioka Y, Katagiri S. State observer-based discrete-time fuzzy control sys-tem[C], IEEE International Symposium on Computational Intelligence in Robotics and Automation(CIRA 2005). Espoo, Finland,2005:531-536.
73. Kim Y J, Kim B S, Lim M T. Finite-time composite control for a class of sin-gularly perturbed nonlinear systems via successive Galerkin approximation [J], IEE Proceedings-Control Theory and Applications,2005.152(5):507-512.
74. Mukaidani H. A new design approach for solving linear quadratic nash games of multiparameter singularly perturbed systems[J], IEEE Transactions on Circuits and Systems I:Regular Papers,2005,52(5):960-974.
75. Sun F C, Hu Y N, Liu H P. Stability analysis and robust controller design for uncer-tain discrete-time singularly perturbed systems[J], Dynamics of Continuous Discrete and Impulsive Systems-Series B-Applications & Algorithms,2005,12(5-6):849-865.
76. Wang J, Li H. Nonlinear PI control of a class of nonlinear singularly perturbed systems[J], IEE Proceedings-Control Theory and Applications,2005,152(5):560-566.
77. Wang X Y, Jiang Y L. A general method for solving singular perturbed impulsive differential equations with two-point boundary conditions[J], Applied Mathematics and Computation,2005,171(2):775-806.
78. Assawinchaichote W, Nguang S K. H∞ fuzzy control design for nonlinear singu-larly perturbed systems with pole placement constraints:an LMI approach[J], IEEE Transactions on Systems. Man and Cybernetics, Part B,2004,34(l):579-588.
79. Assawinchaichote W, Nguang S K, Shi P. H∞ output feedback control design for un-certain fuzzy singularly perturbed systems:an LMI approach[J], Automatica,2004, 40(12):2147-2152.
80. Naidu D S. Singular perturbations and time scales in control theory and applications: An overview[J], Dynamics of Continuous Discrete and Impulsive Systems-Series B-Applications & Algorithms,2002,9(2):233-278.
81. Pan Z, Basar T. H∞-optimal control for singularly perturbed systems. Part Ⅰ:Perfect state measurements[J]. Automatica,1993,29(2):401-423.
82. Pan Z, Basar T. H∞-optimal control for singularly perturbed systems. Ⅱ. Imperfect state measurements[J]. IEEE Transactions on Automatic Control,1994.39(2):280-299.
83. Liu H, Sun F, Sun Z. Stability analysis and synthesis of fuzzy singularly perturbed systems[J], IEEE Transactions on Fuzzy Systems,2005,13(2):273-284.
84. Liu H, Sun F, Hu Y. H∞ control for fuzzy singularly perturbed systems[J], Fuzzy Sets and Systems,2005.155(2):272-291.
85. Sun F, Guo C, Zhao N, et al. Mixed H2/H∞ control of flexible-link manipula-tors based on fuzzy singularly perturbed model[C], The Sixth World Congress on Intelligent Control and Automation(WCICA 2006).2006,1:422-426.
86. Feng W. Characterization and computation for the bound e* in linear time-invariant singularly perturbed systems[J], Systems & Control Letters,1988,11(3):195-202.
87. Chen B S, Lin C L. On the stability bounds of singularly perturbed systems[J], IEEE Transactions on Automatic Control,1990,35(11):1265-1270.
88. Cheng C P. Li T H S, Sun Y Y. Stability margins of singularly perturbed discrete-time systems based on state feedback and linear quadratic optimal control [J], Opti-mal Control Applications and Methods,1992,13(3):227-245.
89. Kafri W S, Abed E H. Stability analysis of discrete-time singularly perturbed sys-tems[J], IEEE Transactions on Circuits and Systems I:Fundamental Theory and Ap-plications,1996,43(10):848-850.
90. Li T H S, Chiou J S, Kung F C. Stability bounds of singularly perturbed discrete systems[J], IEEE Transactions on Automatic Control,1999,44(10):1934-1938.
91. Li T H S, Chiou J S. A new D-stability criterion of multiparameter singu-larly perturbed discrete systems[J], IEEE Transactions on Circuits and Systems I-Fundamental Theory and Applications,2002,49(8):1226-1230.
92. Cao L, Schwartz H M. Complementary results on the stability bounds of singularly perturbed systems[J], IEEE Transactions on Automatic Control,2004,49(11):2017-2021.
93. Ghosh R, Sen S, Datta K B. Method for evaluating stability bounds for discrete-time singularly perturbed systems[J], IEE Proceedings-Control Theory and Applications, 1999,146(2):227-233.
94. Ji Y D, Chizeck H J. Jump linear quadratic gaussian control in continuous-timefJ], IEEE Transactions on Automatic Control,1992,37(12):1884-1892.
95. Stoica A, Yaesh I. Jump Markovian-based control of wing deployment for an un-crewed air vehicle[J], Journal of Guidance Control and Dynamics,2002,25(2):407-411.
96. Cao Y Y. Lam J. Robust H∞, control of uncertain Markovian jump systems with time-delay[J], IEEE Transactions on Automatic Control,2000,45(1):77-83.
97. De Farias D P, Geromel J C, Do Val J B R, et al. Output feedback control of Markov jump linear systems in continuous-time[J], Automatic Control, IEEE Transactions on,2000,45(5):944-949.
98. do Val J B R, Geromel J C, Goncalves A P C. The H-2-control for jump linear systems:cluster observations of the Markov state[J], Automatica,2002,38(2):343-349.
99. do Val J B R, Costa E F. Stabilizability and positiveness of solutions of the jump linear quadratic problem and the coupled algebraic Riccati equation[J], IEEE Trans-actions on Automatic Control,2005.50(5):691-695.
100. Bouhtouri A E, Hadri K E. Robust stabilization of jump linear systems with mul-tiplicative noise[J], IMA Journal of Mathematical Control and Information,2003, 20(1):1.
101. Chen W H, Xu J X, Guan Z H. Guaranteed cost control for uncertain Marko-vian jump systems with mode-dependent time-delays[J], IEEE Transactions on Au-tomatic Control,2003,48(12):2270-2277.
102. de Souza C E. Robust stability and stabilization of uncertain discrete-time Markovian jump linear systems[J], IEEE Transactions on Automatic Control.2006, 51(5):836-841.
103. Lee J W, Dullerud G E. Optimal disturbance attenuation for discrete-time switched and Markovian jump linear systems[J], SIAM Journal on Control and Optimization, 2006,45(4):1329-1358.
104. Li L, Ugrinovskii V A. On necessary and sufficient conditions for H∞ output feed-back control of Markov jump linear systems[J], IEEE Transactions on Automatic Control,2007,52(7):1287-1292.
105. Lee J W, Khargonekar P P. Optimal Output Regulation for Discrete-Time Switched and Markovian Jump Linear Systems[J], SIAM Journal on Control and Optimiza-tion,2008,47(1):40-72.
106. Todorov M G, Fragoso M D. Output Feedback H∞ Control of Continuous-Time Infinite Markovian Jump Linear Systems via LMI Methods[J], SIAM Journal on Control and Optimization,2008,47(2):950-974.
107. Tan S P, Zhang J F, Yao L L. Optimality analysis of adaptive sampled control of hybrid systems with quadratic index[J], IEEE Transactions on Automatic Control, 2005.50(7):1044-1051.
108. El Ghaoui L. Rami M A. Robust state-feedback stabilization of jump linear sys-tems via LMIs[J], International Journal of Robust and Nonlinear Control,1996,6(9-10):1015-1022.
109. Stoica A M, Yaesh I. Markovian jump delayed Hopfield networks with multiplica-tive noise[J], Automatica,2008,44(8):2157-2162.
110. Yue D, Han Q L. Delay-dependent exponential stability of stochastic systems with time-varying delay, nonlinearity, and Markovian switching[J], IEEE Transactions on Automatic Control,2005,50(2):217-222.
111. Nguang S K, Assawinchaichote W, Shi P, et al. Robust H∞ control design for uncertain fuzzy systems with Markovian jumps:an LMI approach[C], American Control Conference. Portland, OR, USA,2005,3:1805-1810.
112. Wu H N, Cai K Y. Mode-independent robust stabilization for uncertain Markovian jump nonlinear systems via fuzzy control [J], IEEE Transactions on Systems, Man and Cybernetics, Part B,2006,36(3):509-519.
113. Wu H N, Cai K Y. Robust fuzzy control for uncertain discrete-time nonlinear Markovian jump systems without mode observations [J], Information Sciences,2007, 177(6):1509-1522.
114. Wu H N. Reliable robust H∞ fuzzy control for uncertain nonlinear systems with Markovian jumping actuator faults[J], Journal of Dynamic Systems, Measurement, and Control,2007,129:252.
115. Arrifano N S D, Oliveira V A. Robust H∞ fuzzy control design for Markovian jump systems[C], CDC-ECC'05. Seville, Spain,2005:3243-3248.
116. Gahinet P, Nemirovski A, Laub A J, et al. LMI Control Toolbox[M], Natick, MA: The Math Works, Inc.,1995.
117. Zhou S, Feng G, Lam J, et al. Robust H∞ control for discrete-time fuzzy sys-tems via basis-dependent Lyapunov functions[J], Information Sciences,2005,174(3-4):197-217.
118. Choi D J, Park P. H∞ state-feedback controller design for discrete-time fuzzy sys-tems using fuzzy weighting-dependent Lyapunov functions[J], IEEE Transactions on Fuzzy Systems,2003,11(2):271-278.
119. Chen B S, Tseng C S, Uang H J. Mixed H2/H∞ fuzzy output feedback control design for nonlinear dynamic systems:an LMI approach[J], IEEE Transactions on Fuzzy Systems,2000.8(3):249-265.
120. Han Z X, Feng G, Walcott B L. et al. Dynamic output feedback controller design for fuzzy systems[J], IEEE Transactions on Systems, Man and Cybernetics, Part B, 2000.30(1):204-210.
121. Zheng F, Wang Q G, Lee T H, et al. Robust PI controller design for nonlinear systems via fuzzy modeling approach[J], IEEE Transactions on Systems. Man and Cybernetics, Part A.,2001,31(6):666-675.
122. Katayama H, Ichikawa A. H∞ control for discrete-time Takagi-Sugeno fuzzy sys-tems[J]. International Journal of Systems Science,2002,33(14):1099-1107.
123. Nguang S K, Shi P. Fuzzy output feedback control of nonlinear systems under sampled measurements [J], Automatica,2003,39(12):2169-2174.
124. Lin M L, Lo J C. An iterative solution to dynamic output stabilization and com-ments on "Dynamic output feedback controller design for fuzzy systems"[J], IEEE Transactions on Systems, Man and Cybernetics. Part B,2004,34(1):679-681.
125. Chen S S, Chang Y C, Su S F, et al. Robust static output-feedback stabilization for nonlinear discrete-time systems with time delay via fuzzy control approach[J], IEEE Transactions on Fuzzy Systems,2005,13(2):263-272.
126. Cao Y Y, Lam J, Sun Y X. Static output feedback stabilization:An ILMI ap-proach[J]. Automatica,1998,34(12):1641-1645.
127. Wu H N, Zhang H Y. Reliable mixed L2/H∞ fuzzy static output feedback control for nonlinear systems with sensor faults[J], Automatica,2005,41(11):1925-1932.
128. Lo J C, Lin M L. Robust H∞ nonlinear control via fuzzy static output feedback[J], IEEE Transactions on Circuits and Systems I:Fundamental Theory and Applica-tions,2003,50(11):1494-1502.
129. Kau S W, Lee H J, Yang C M, et al. Robust H∞ fuzzy static output feedback con-trol of T-S fuzzy systems with parametric uncertainties[J]. Fuzzy Sets and Systems. 2007,158(2):135-146.
130. Crusius C A R, Trofino A. Sufficient LMI conditions for output feedback control problems[J], IEEE Transactions on Automatic Control,1999,44(5):1053-1057.
131. Apkarian P, Hoang Duong T, Bernussou J. Continuous-time analysis, eigenstruc-ture assignment, and H2 synthesis with enhanced linear matrix inequalities (LMI) characterizations[J], IEEE Transactions on Automatic Control,2001,46(12):1941-1946.
132. Liu X, Zhang Q. Approaches to quadratic stability conditions and H∞ con-trol designs for T-S fuzzy systems[J], IEEE Transactions on Fuzzy Systems,2003, 11(6):830-839.
133. Boyd S, Ghaoui L E, Feron E, et al. Linear Matrix Inequalities in System and Control Theory[M], Philadelphia:Society for Industrial and Applied Mathematics, PA:SIAM.1994.
134. Ding B, Sun H, Yang P. Further studies on LMI-based relaxed stabilization conditions for nonlinear systems in Takagi-Sugeno's form[J], Automatica,2006, 42(3):503-508.
135. Yang B, Yu D C, Feng G, et al. Stabilisation of a class of nonlinear continuous time systems by a fuzzy control approach [J], IEE Proceedings-Control Theory and Applications,2006,153(4):427-436.
136. Wu H N, Cai K Y. H2 guaranteed cost fuzzy control design for discrete-time non-linear systems with parameter uncertainty [J], Automatica,2006,42(7):1183-1188.
137. Lee H J, Park J B, Joo Y H. Robust load-frequency control for uncertain non-linear power systems:A fuzzy logic approach[J], Information Sciences,2006, 176(23):3520-3537.
138. Ting C S. Stability analysis and design of Takagi-Sugeno fuzzy systems[J], Infor-mation Sciences,2006,176(19):2817-2845.
139. Ohtake H, Tanaka K, Wang H O. Switching fuzzy controller design based on switching Lyapunov function for a class of nonlinear systems[J], IEEE Transactions on Systems, Man and Cybernetics. Part B,2006,36(l):13-23.
140. Yu G R. Chen S H. Nonlinear flight control of a Two-Degree-of-Freedom he-licopter using Takagi-Sugeno fuzzy model[C], IEEE International Conference on Systems, Man and Cybernetics. Taiwan, China,2006,5:4354-4359.
141. Lian K Y, Su C H. Huang C S. Performance enhancement for T-S fuzzy control using neural networks[J], IEEE Transactions on Fuzzy Systems,2006,14(5):619-627.
142. Wang W J, Sun C H. A relaxed stability criterion for T-S fuzzy discrete systems[J], IEEE Transactions on Systems. Man and Cybernetics, Part B,2004,34(5):2155-2158.
143. Huang D, Nguang S K. Static output feedback controller design for fuzzy systems: An ILMI approach[J], Information Sciences,2007,177(14):3005-3015.
144. Chen B, Liu X, Tong S. Delay-dependent stability analysis and control synthe-sis of fuzzy dynamic systems with time delay[J], Fuzzy Sets and Systems,2006. 157(16):2224-2240.
145. Choi D J, Park P, Chang M S. A dynamic output-feedback variable structure controller design for uncertain fuzzy systems[C], IEEE International Conference on Systems, Man and Cybernetics.2003,1:804-809.
146. Lam J, Zhou S. Dynamic output feedback H∞ control of discrete-time fuzzy sys-tems:a fuzzy-basis-dependent Lyapunov function approach[J]. International Journal of Systems Science,2007.38(1):25-37.
147. Li J, Wang H O, Niemann D, et al. Dynamic parallel distributed compensation for Takagi-Sugeno fuzzy systems:An LMI approach[J], Information Sciences,2000, 123(3-4):201-221.
148. Tanaka K, Yamauchi K, Ohtake H, et al. Optimal dynamic output feedback de-signs for backing-up control of a vehicle with triple trailers[C], IEEE International Conference on Fuzzy Systems. Vancouver, BC, Canada,2006:2385-2391.
149. Tuan H D. Apkarian P. Narikiyo T, et al. New fuzzy control model and dynamic output feedback parallel distributed compensation[J], IEEE Transactions on Fuzzy Systems,2004,12(1):13-21.
150. Xu S, Lam J. Robust H∞ control for uncertain discrete-time-delay fuzzy sys-tems via output feedback controllers[J], IEEE Transactions on Fuzzy Systems,2005, 13(1):82-93.
151. Yoneyama J. Robust H∞ control analysis and synthesis for Takagi-Sugeno general uncertain fuzzy systems[J], Fuzzy Sets and Systems,2006,157(16):2205-2223.
152. Nguang S K, Shi P. H∞ fuzzy output feedback control design for nonlinear sys-tems:an LMI approach[J], IEEE Transactions on Fuzzy Systems,2003,11(3):331-340.
153. Wu H N, Cai K Y. H2 guaranteed cost fuzzy control for uncertain nonlinear systems via linear matrix inequalities [J], Fuzzy Sets and Systems,2004,148(3):411-429.
154. Dong J, Yang G H. Static output feedback control synthesis for linear systems with time-invariant parametric uncertainties[J], IEEE Transactions on Automatic Control, 2007,52(10):1930-1936.
155. Dong J, Yang G H. Static output feedback control synthesis for discrete-time T-S fuzzy systems[J], International Journal of Control Automation and Systems,2007, 5(3):349-354.
156. Chilali M, Gahinet P. H∞ design with pole placement constraints:an LMI ap-proach[J], IEEE Transactions on Automatic Control,1996,41(3):358-367.
157. Nguang S K, Shi P. Robust H∞ output feedback control design for fuzzy dynamic systems with quadratic D stability constraints:An LMI approach[J], Information Sciences,2006,176(15):2161-2191.
158. Wang L, Feng G. Piecewise H.x controller design of discrete time fuzzy sys-tems[J], IEEE Transactions on Systems, Man and Cybernetics, Part B,2004, 34(1):682-686.
159. Wang H O, Tanaka K. Griffin M F. An approach to fuzzy control of nonlinear systems:stability and design issues[J], IEEE Transactions on Fuzzy Systems,1996, 4(1):14-23.
160. Delmotte F, Guerra T M, Ksantini M. Continuous Takagi-Sugeno's models:re-duction of the number of LMI conditions in various fuzzy control design technics[J], IEEE Transactions on Fuzzy Systems,2007,15(3):426-438.
161. Teixeira M C M, Zak S H. Stabilizing controller design for uncertain nonlinear sys-tems using fuzzy models[J], IEEE Transactions on Fuzzy Systems,1999,7(2):133-142.
162. Chen B, Liu X, Tong S, et al. Guaranteed cost control of T-S fuzzy systems with state and input delays[J], Fuzzy Sets and Systems,2007.158(20):2251-2267.
163. Petersen I R, McFarlane D C. Optimal guaranteed cost control and filtering for uncertain linear systems[J], IEEE Transactions on Automatic Control,1994, 39(9):1971-1977.
164. Pawluszewicz E, Bartosiewicz Z. Euler' discretization and dynamic equivalence of nonlinear control systems[M], Nonlinear control. Springer Berlin/Heidelberg,2001, 2:183-191.
165. Fridman E. A descriptor system approach to nonlinear singularly perturbed optimal control problem[J], Automatica,2001.37(4):543-549.
166. Fridman E. Effects of small delays on stability of singularly perturbed systems[J], Automatica,2002,38(5):897-902.
167. Shi P, Dragan V. Asymptotic H∞ control of singularly perturbed systems with parametric uncertainties[J], IEEE Transactions on Automatic Control,1999. 44(9):1738-1742.
168. Garcia G, Daafouz J, Bernussou J. The infinite time near optimal decentralized reg-ulator problem for singularly perturbed systems:a convex optimization approach[J], Automatica,2002,38(8):1397-1406.
169. Fridman E. Robust sampled-data H∞ control of linear singularly perturbed sys-tems[J], IEEE Transactions on Automatic Control.2006.51(3):470-475.
170. Assawinchaichote W, Nguang S K, Shi P. Robust H∞ fuzzy filter design for un-certain nonlinear singularly perturbed systems with Markovian jumps:An LMI ap-proach[J]. Information Sciences,2007,177(7):1699-1714.
171. Saksena V R, Cruz J, J. Stabilization of singularly perturbed linear time-invariant systems using low-order observers[J], IEEE Transactions on Automatic Control, 1981,26(2):510-513.
172. Chen Y, Liu Y. Summary of singular perturbation modeling of multi-time scale power systems[C], Transmission and Distribution Conference and Exhibition:Asia and Pacific. Dalian, China,2005:1-1.
173. Lizarraga I, Etxebarria V. Combined PD-H∞ approach to control of flexible link manipulators using only directly measurable variables[J], Cybernetics and Systems, 2003,34(1):19-31.
174. Sandell N R. Robust stability of systems with application to singular perturba-tions[J], Automatica,1979,15(4):467-470.
175. Shao Z H, Sawan M E. Robust stability of singularly perturbed systems[J], Inter-national Journal of Control,1993,58(6):1469-1476.
176. Sen S, Datta K B. Stability bounds of singularity perturbed systems[J], IEEE Transactions on Automatic Control,1993,38(2):302-304.
177. Mustafa D, Davidson T N. Block bialternate sum and associated stability formu-lae[J], Automatica,1995,31(9):1263-1274.
178. Isidori A. H∞ control via measurement feedback for affine nonlinear systems[J], International Journal of Robust and Nonlinear Control,1994,4(4):553-574.
179. Zak S H, Maccarley C. State-feedback control of non-linear systems[J], Interna-tional Journal of Control 1986,43:1497-1514.
180. Lin W, Byrnes C I. H∞-control of discrete-time nonlinear systems[J], IEEE Trans-actions on Automatic Control,1996,41(4):494-510.
181. Boyd S, Vandenberghe L. Convex Optimization[M], Cambridge University Press, 2004.
182. Wu H N. Reliable LQ fuzzy control for nonlinear discrete-time systems via LMIs[J], IEEE Transactions on Systems, Man and Cybernetics, Part B,2004, 34(2):1270-1275.
183. Feng G. Approaches to quadratic stabilization of uncertain fuzzy dynamic sys-tems[J], IEEE Transactions on Circuits and Systems I:Fundamental Theory and Ap-plications,2001,48(6):760-769.
184. Feng G, Chen C L, Sun D, et al. H∞ controller synthesis of fuzzy dynamic systems based on piecewise Lyapunov functions and bilinear matrix inequalities[J], IEEE Transactions on Fuzzy Systems,2005.13(1):94-103.
185. Pan G L, BarShalom Y. Stabilization of jump linear Gaussian systems without mode observations[J], International Journal of Control,1996,64(4):631-661.
2.张天平.基于一种修改的李亚普诺夫函数的自适应模糊滑模控制[Jl,自动化学报，2002,28(1)：137-142.
3.应浩.关于模糊控制理论与应用的若干问题[J],自动化学报,2001,27(4)：591-592.
4.孙增圻.基于模糊状态模型的连续系统控制器设计和稳定性分析[J],自动化学报.1998,24(2)：212-216.
5.张松涛,任光.基于分段模糊Lyapunov方法的离散模糊系统分析与设计[J],自动化学报.2006,32(5)：813-818.
6.刘亚,胡寿松.不确定非线性系统的模糊鲁棒跟踪控制[J],自动化学报,2004,30(6)：949-953.
7.修智宏,任光.T-S模糊控制系统的稳定性分析及系统化设计[J],自动化学报,2004,30(5)：731-740.
8.胡包钢,应浩.模糊PID控制技术研究发展回顾及其面临的若干重要问题[J]，Acta Automatica Sinica,2001,27(4):567-584.
9.邱焕耀,毛宗源.采用模糊控制的感应电动机解耦变结构系统的研究[Jl,自动化学报，1998,24(3)：391-394.
10.姚尹武，熊金涛.一种神经网络自组织模糊控制[J],控制理论与应用,1996,13(6)：738-744.
11.张金明,李人厚.模糊控制的系统化设计和稳定性分析[J]，自动化学报,1999,25(4)：493-497.
12.丁海山,毛剑琴,林岩.基于模糊树模型的自适应直接逆控制[J],自动化学报,2008,34(5)：574-580.
13.罗艳斌,曹永岩，孙优贤.具有时变输入时滞的不确定TS模糊系统的鲁棒稳定性[J],自动化学报,2008,87-92：1.
14.巩长忠.王伟,刘全利.基于观测器的非线性不确定离散系统的鲁棒模糊控制[J],控制理论与应用,2005,22(1)：96-100.
15.丁宝苍，孙鹤旭,乔玉娥.基于参数Lyapunov函数的T-S模糊控制系统的稳定性分析[J],自动化学报,2005,31(4)：651-654.
16.李祖欣,王万良，雷必成,陈惠英.网络控制系统中基于模糊反馈的消息调度[J],自动化学报,2007，33(11)：1229-1232.
17.刘华平,孙富春，孙增圻.李春文.基于部分状态信息的模糊控制器设计[J],自动化学报,2004,30(6)：999-1003.
18.张化光.王智良,黎明,全永兵，张明君.广义模糊双曲正切模型：一个万能逼近器[J],自动化学报,2004,30(3)：416-422.
19.张大庆,张庆灵,胡跃冰.TS模糊系统稳定性的一个新的充分条件[J],自动化学报,2007,33(2)：222-224.
20. Takagi T. Sugeno M. Fuzzy identification of systems and its applications to mod-eling and control[J], IEEE Transactions on Systems, Man and Cybernetics,1985, SMC-15(1):116-132.
21. Cao S G, Rees N W, Feng G. Analysis and design for a class of complex control sys-tems Part Ⅰ:Fuzzy modelling and identification[J], Automatica,1997,33(6):1017-1028.
22. Johansen T A, Shorten R, Murray-Smith R. On the interpretation and identification of dynamic Takagi-Sugeno fuzzy models[J], IEEE Transactions on Fuzzy Systems, 2000,8(3):297-313.
23. Tanaka K, Wang H O. Fuzzy Control Systems Design and Analysis:A Linear Matrix Inequality Approach[M], New York, NY, USA:John Wiley & Sons, Inc., 2001.
24. Ying H. General SISO Takagi-Sugeno fuzzy systems with linear rule consequent are universal approximators[J]. IEEE Transactions on Fuzzy Systems,1998,6(4):582-587.
25. Zeng K. Zhang N Y, Xu W L. A comparative study on sufficient conditions for Takagi-Sugeno fuzzy systems as universal approximators[J], IEEE Transactions on Fuzzy Systems,2000,8(6):773-780.
26. Feng G. A survey on analysis and design of model-based fuzzy control systems[J], IEEE Transactions on Fuzzy Systems.2006,14(5):676-697.
27. Sala A, Guerra T M, Babuska R. Perspectives of fuzzy systems and control[J], Fuzzy Sets and Systems,2005,156(3):432-444.
28. Fang C H, Liu Y S, Kau S W, et al. A new LMI-based approach to relaxed quadratic stabilization of T-S fuzzy control systems[J], IEEE Transactions on Fuzzy Systems. 2006,14(3):386-397.
29. Ho D W C, Niu Y. Robust fuzzy design for nonlinear uncertain stochastic systems via sliding-mode control[J], IEEE Transactions on Fuzzy Systems.2007,15(3):350-358.
30. Huang D, Nguang S K. Robust H∞ static output feedback control of fuzzy systems: an ILMI approach[J], IEEE Transactions on Systems, Man and Cybernetics, Part B, 2006,36(1):216-222.
31. Kim E, Lee H. New approaches to relaxed quadratic stability condition of fuzzy control systems[J], IEEE Transactions on Fuzzy Systems,2000,8(5):523-534.
32. Li T H S, Tsai S H. T-S fuzzy bilinear model and fuzzy controller design for a class of nonlinear systems[J], IEEE Transactions on Fuzzy Systems,2007,15(3):494-506.
33. Lian K Y, Liou J J. Output tracking control for fuzzy systems via output feedback design[J], IEEE Transactions on Fuzzy Systems,2006,14(5):628-639.
34. Liu X, Zhang Q. New approaches to H∞ controller designs based on fuzzy observers for T-S fuzzy systems via LMI[J], Automatica,2003,39(9):1571-1582.
35. Sala A, Arino C. Asymptotically necessary and sufficient conditions for stability and performance in fuzzy control:Applications of Polya's theorem[J], Fuzzy Sets and Systems,2007,158(24):2671-2686.
36. Tanaka K, Ikeda T, Wang H O. Fuzzy regulators and fuzzy observers:relaxed stability conditions and LMI-based designs[J], IEEE Transactions on Fuzzy Systems, 1998.6(2):250-265.
37. Teixeira M C M, Assuncao E. Avellar R G. On relaxed LMI-based designs for fuzzy regulators and fuzzy observers[J], IEEE Transactions on Fuzzy Systems,2003, 11(5):613-623.
38. Tuan H D. Apkarian P, Narikiyo T, et al. Parameterized linear matrix inequality techniques in fuzzy control system design[J], IEEE Transactions on Fuzzy Systems, 2001,9(2):324-332.
39. Tseng C S, Hwang C K. Fuzzy observer-based fuzzy control design for nonlin-ear systems with persistent bounded disturbances [J], Fuzzy Sets and Systems,2007, 158(2):164-179.
40. Tanaka K, Hori T, Wang H O. A multiple Lyapunov function approach to stabi-lization of fuzzy control systems[J], IEEE Transactions on Fuzzy Systems,2003, 11(4):582-589.
41. Wang W J, Chen Y J, Sun C H. Relaxed stabilization criteria for discrete-time T-S fuzzy control systems based on a switching fuzzy model and piecewise Lyapunov function[J], IEEE Transactions on Systems, Man and Cybernetics, Part B,2007, 37(3):551-559.
42. Wang W J, Sun C H. Relaxed stability and stabilization conditions for a T-S fuzzy discrete system[J], Fuzzy Sets and Systems.2005,156(2):208-225.
43. Guerra T M, Vermeiren L. LMI-based relaxed nonquadratic stabilization conditions for nonlinear systems in the Takagi-Sugeno's form[J], Automatica,2004,40(5):823-829.
44. Johansson M, Rantzer A, Arzen K E. Piecewise quadratic stability of fuzzy sys-tems[J], IEEE Transactions on Fuzzy Systems,1999,7(6):713-722.
45. Feng G. Controller synthesis of fuzzy dynamic systems based on piecewise Lya-punov functions[J], IEEE Transactions on Fuzzy Systems,2003,11(5):605-612.
46. Feng G. H∞ controller design of fuzzy dynamic systems based on piecewise Lya-punov functions[J], IEEE Transactions on Systems, Man and Cybernetics, Part B, 2004,34(1):283-292.
47. Feng G. Stability analysis of discrete-time fuzzy dynamic systems based on piece-wise Lyapunov functions[J], IEEE Transactions on Fuzzy Systems,2004,12(1):22-28.
48. Chen C L, Feng G, Sun D, et al. H∞ output feedback control of discrete-time fuzzy systems with application to chaos control[J], IEEE Transactions on Fuzzy Systems, 2005,13(4):531-543.
49. Kruszewski A, Wang R, Guerra T M. Nonquadratic stabilization conditions for a class of uncertain nonlinear discrete time TS fuzzy models:a new approach[J], IEEE Transactions on Automatic Control,2008,53(2):606-611.
50. Kokotovic P V, O'Reilly J, Khalil H K. Singular Perturbation Methods in Control: Analysis and Design[M], Orlando, FL, USA:Academic Press, Inc.,1986.
51. Dong J, Yang G H. H∞ control for fast sampling discrete-time singularly perturbed systems[J], Automatica,2008,44(5):1385-1393.
52. Dong J, Yang G H. Robust H∞ control for standard discrete-time singu-larly perturbed systems[J], IEE Proceedings-Control Theory & Applications,2007. 1(4):1141-1148.
53. Du Z. Singularly perturbed third-order boundary value problem for nonlinear sys-tems[J], Applied Mathematics and Computation,2007,189(1):869-877.
54. Li T H S, Lin K J. Composite fuzzy control of nonlinear singularly perturbed sys-tems[J], IEEE Transactions on Fuzzy Systems,2007.15(2):176-187.
55. Mukaidani H. A numerical algorithm for finding solution of sign-indefinite alge-braic Riccati equations for general multiparameter singularly perturbed systems[J], Applied Mathematics and Computation,2007,189(1):255-270.
56. Assawinchaichote W, Nguang S K. Fuzzy H∞ output feedback control design for singularly perturbed systems with pole placement constraints:an LMI approach[J], IEEE Transactions on Fuzzy Systems,2006,14(3):361-371.
57. Lin K J, Li T H S. Stabilization of uncertain singularly perturbed systems with pole-placement constraints[J], IEEE Transactions On Circuits And Systems II-Express Briefs.2006.53(9):916-920.
58. Lu G, Ho D W C. Generalized quadratic stability for continuous-time singular systems with nonlinear perturbation[J]. IEEE Transactions on Automatic Control, 2006,51 (5):818-823.
59. Nair J M, Lazar A, Bandyopadhyay B. Robust control for uncertain singularly perturbed systems using periodic output feedback[C], American Control Conference. Minneapolis, MN, United States:2006:4326-4331.
60. Shao Z H, Sawan M E. Stabilisation of uncertain singularly perturbed systems[J], IEE Proceedings-Control Theory and Applications,2006,153(1):99-103.
61. Son J W, Lim J T. Robust stability of nonlinear singularly perturbed system with un-certainties[J], IEE Proceedings-Control Theory and Applications,2006,153(1):104-110.
62. Choi H L, Shin Y S, Lim J T. Control of nonlinear singularly perturbed systems using feedback linearisation[J], IEE Proceedings-Control Theory and Applications, 2005,152(1):91-94.
63. Li T H S, Lin K J. Stabilization of singularly perturbed fuzzy systems[J], IEEE Transactions on Fuzzy Systems,2004,12(5):579-595.
64. Shao Z H. Robust stability of two-time-scale systems with nonlinear uncertain-ties[J], IEEE Transactions on Automatic Control.2004,49(2):258-261.
65. Hsiao F H, Hwang J D, Pan S T. D-stability problem of discrete singularly perturbed systems[J], International Journal of Systems Science,2003,34(3):227-236.
66. Datta K B, RaiChaudhuri A. H2/H∞ control of discrete singularly perturbed sys-tems:the state feedback case[J], Automatica,2002,38(10):1791-1797.
67. Kim B S, Kim Y J. Lim M T. LQG control for nonstandard singularly perturbed discrete time systems[C], Proc.41st IEEE Conf. Decision and Control. Las Vegas, Nevada USA,2002.4:3736-3741.
68. Lim M T, Kang C G, Kim B S. Optimal control of linear nonstandard singu-larly perturbed discrete systems[J], Dynamics of Continuous Discrete and Impulsive Systems-Series B-Applications & Algorithms,2002,9(2):163-174.
69. Fridman E. Near-optimal H∞ control of linear singularly perturbed systems[J], IEEE Transactions on Automatic Control,1996,41 (2):236-240.
70. Gajic Z, Koskie S, Coumarbatch C. On the singularly perturbed matrix differ-ential Riccati equation[C], The 44th IEEE Conference on Decision and Control. 2005:3638-3644.
71. Guan Z H, Hill D J, Shen X. On hybrid impulsive and switching systems and ap-plication to nonlinear control[J], IEEE Transactions on Automatic Control,2005, 50(7):1058-1062.
72. Han H, Morioka Y, Katagiri S. State observer-based discrete-time fuzzy control sys-tem[C], IEEE International Symposium on Computational Intelligence in Robotics and Automation(CIRA 2005). Espoo, Finland,2005:531-536.
73. Kim Y J, Kim B S, Lim M T. Finite-time composite control for a class of sin-gularly perturbed nonlinear systems via successive Galerkin approximation [J], IEE Proceedings-Control Theory and Applications,2005.152(5):507-512.
74. Mukaidani H. A new design approach for solving linear quadratic nash games of multiparameter singularly perturbed systems[J], IEEE Transactions on Circuits and Systems I:Regular Papers,2005,52(5):960-974.
75. Sun F C, Hu Y N, Liu H P. Stability analysis and robust controller design for uncer-tain discrete-time singularly perturbed systems[J], Dynamics of Continuous Discrete and Impulsive Systems-Series B-Applications & Algorithms,2005,12(5-6):849-865.
76. Wang J, Li H. Nonlinear PI control of a class of nonlinear singularly perturbed systems[J], IEE Proceedings-Control Theory and Applications,2005,152(5):560-566.
77. Wang X Y, Jiang Y L. A general method for solving singular perturbed impulsive differential equations with two-point boundary conditions[J], Applied Mathematics and Computation,2005,171(2):775-806.
78. Assawinchaichote W, Nguang S K. H∞ fuzzy control design for nonlinear singu-larly perturbed systems with pole placement constraints:an LMI approach[J], IEEE Transactions on Systems. Man and Cybernetics, Part B,2004,34(l):579-588.
79. Assawinchaichote W, Nguang S K, Shi P. H∞ output feedback control design for un-certain fuzzy singularly perturbed systems:an LMI approach[J], Automatica,2004, 40(12):2147-2152.
80. Naidu D S. Singular perturbations and time scales in control theory and applications: An overview[J], Dynamics of Continuous Discrete and Impulsive Systems-Series B-Applications & Algorithms,2002,9(2):233-278.
81. Pan Z, Basar T. H∞-optimal control for singularly perturbed systems. Part Ⅰ:Perfect state measurements[J]. Automatica,1993,29(2):401-423.
82. Pan Z, Basar T. H∞-optimal control for singularly perturbed systems. Ⅱ. Imperfect state measurements[J]. IEEE Transactions on Automatic Control,1994.39(2):280-299.
83. Liu H, Sun F, Sun Z. Stability analysis and synthesis of fuzzy singularly perturbed systems[J], IEEE Transactions on Fuzzy Systems,2005,13(2):273-284.
84. Liu H, Sun F, Hu Y. H∞ control for fuzzy singularly perturbed systems[J], Fuzzy Sets and Systems,2005.155(2):272-291.
85. Sun F, Guo C, Zhao N, et al. Mixed H2/H∞ control of flexible-link manipula-tors based on fuzzy singularly perturbed model[C], The Sixth World Congress on Intelligent Control and Automation(WCICA 2006).2006,1:422-426.
86. Feng W. Characterization and computation for the bound e* in linear time-invariant singularly perturbed systems[J], Systems & Control Letters,1988,11(3):195-202.
87. Chen B S, Lin C L. On the stability bounds of singularly perturbed systems[J], IEEE Transactions on Automatic Control,1990,35(11):1265-1270.
88. Cheng C P. Li T H S, Sun Y Y. Stability margins of singularly perturbed discrete-time systems based on state feedback and linear quadratic optimal control [J], Opti-mal Control Applications and Methods,1992,13(3):227-245.
89. Kafri W S, Abed E H. Stability analysis of discrete-time singularly perturbed sys-tems[J], IEEE Transactions on Circuits and Systems I:Fundamental Theory and Ap-plications,1996,43(10):848-850.
90. Li T H S, Chiou J S, Kung F C. Stability bounds of singularly perturbed discrete systems[J], IEEE Transactions on Automatic Control,1999,44(10):1934-1938.
91. Li T H S, Chiou J S. A new D-stability criterion of multiparameter singu-larly perturbed discrete systems[J], IEEE Transactions on Circuits and Systems I-Fundamental Theory and Applications,2002,49(8):1226-1230.
92. Cao L, Schwartz H M. Complementary results on the stability bounds of singularly perturbed systems[J], IEEE Transactions on Automatic Control,2004,49(11):2017-2021.
93. Ghosh R, Sen S, Datta K B. Method for evaluating stability bounds for discrete-time singularly perturbed systems[J], IEE Proceedings-Control Theory and Applications, 1999,146(2):227-233.
94. Ji Y D, Chizeck H J. Jump linear quadratic gaussian control in continuous-timefJ], IEEE Transactions on Automatic Control,1992,37(12):1884-1892.
95. Stoica A, Yaesh I. Jump Markovian-based control of wing deployment for an un-crewed air vehicle[J], Journal of Guidance Control and Dynamics,2002,25(2):407-411.
96. Cao Y Y. Lam J. Robust H∞, control of uncertain Markovian jump systems with time-delay[J], IEEE Transactions on Automatic Control,2000,45(1):77-83.
97. De Farias D P, Geromel J C, Do Val J B R, et al. Output feedback control of Markov jump linear systems in continuous-time[J], Automatic Control, IEEE Transactions on,2000,45(5):944-949.
98. do Val J B R, Geromel J C, Goncalves A P C. The H-2-control for jump linear systems:cluster observations of the Markov state[J], Automatica,2002,38(2):343-349.
99. do Val J B R, Costa E F. Stabilizability and positiveness of solutions of the jump linear quadratic problem and the coupled algebraic Riccati equation[J], IEEE Trans-actions on Automatic Control,2005.50(5):691-695.
100. Bouhtouri A E, Hadri K E. Robust stabilization of jump linear systems with mul-tiplicative noise[J], IMA Journal of Mathematical Control and Information,2003, 20(1):1.
101. Chen W H, Xu J X, Guan Z H. Guaranteed cost control for uncertain Marko-vian jump systems with mode-dependent time-delays[J], IEEE Transactions on Au-tomatic Control,2003,48(12):2270-2277.
102. de Souza C E. Robust stability and stabilization of uncertain discrete-time Markovian jump linear systems[J], IEEE Transactions on Automatic Control.2006, 51(5):836-841.
103. Lee J W, Dullerud G E. Optimal disturbance attenuation for discrete-time switched and Markovian jump linear systems[J], SIAM Journal on Control and Optimization, 2006,45(4):1329-1358.
104. Li L, Ugrinovskii V A. On necessary and sufficient conditions for H∞ output feed-back control of Markov jump linear systems[J], IEEE Transactions on Automatic Control,2007,52(7):1287-1292.
105. Lee J W, Khargonekar P P. Optimal Output Regulation for Discrete-Time Switched and Markovian Jump Linear Systems[J], SIAM Journal on Control and Optimiza-tion,2008,47(1):40-72.
106. Todorov M G, Fragoso M D. Output Feedback H∞ Control of Continuous-Time Infinite Markovian Jump Linear Systems via LMI Methods[J], SIAM Journal on Control and Optimization,2008,47(2):950-974.
107. Tan S P, Zhang J F, Yao L L. Optimality analysis of adaptive sampled control of hybrid systems with quadratic index[J], IEEE Transactions on Automatic Control, 2005.50(7):1044-1051.
108. El Ghaoui L. Rami M A. Robust state-feedback stabilization of jump linear sys-tems via LMIs[J], International Journal of Robust and Nonlinear Control,1996,6(9-10):1015-1022.
109. Stoica A M, Yaesh I. Markovian jump delayed Hopfield networks with multiplica-tive noise[J], Automatica,2008,44(8):2157-2162.
110. Yue D, Han Q L. Delay-dependent exponential stability of stochastic systems with time-varying delay, nonlinearity, and Markovian switching[J], IEEE Transactions on Automatic Control,2005,50(2):217-222.
111. Nguang S K, Assawinchaichote W, Shi P, et al. Robust H∞ control design for uncertain fuzzy systems with Markovian jumps:an LMI approach[C], American Control Conference. Portland, OR, USA,2005,3:1805-1810.
112. Wu H N, Cai K Y. Mode-independent robust stabilization for uncertain Markovian jump nonlinear systems via fuzzy control [J], IEEE Transactions on Systems, Man and Cybernetics, Part B,2006,36(3):509-519.
113. Wu H N, Cai K Y. Robust fuzzy control for uncertain discrete-time nonlinear Markovian jump systems without mode observations [J], Information Sciences,2007, 177(6):1509-1522.
114. Wu H N. Reliable robust H∞ fuzzy control for uncertain nonlinear systems with Markovian jumping actuator faults[J], Journal of Dynamic Systems, Measurement, and Control,2007,129:252.
115. Arrifano N S D, Oliveira V A. Robust H∞ fuzzy control design for Markovian jump systems[C], CDC-ECC'05. Seville, Spain,2005:3243-3248.
116. Gahinet P, Nemirovski A, Laub A J, et al. LMI Control Toolbox[M], Natick, MA: The Math Works, Inc.,1995.
117. Zhou S, Feng G, Lam J, et al. Robust H∞ control for discrete-time fuzzy sys-tems via basis-dependent Lyapunov functions[J], Information Sciences,2005,174(3-4):197-217.
118. Choi D J, Park P. H∞ state-feedback controller design for discrete-time fuzzy sys-tems using fuzzy weighting-dependent Lyapunov functions[J], IEEE Transactions on Fuzzy Systems,2003,11(2):271-278.
119. Chen B S, Tseng C S, Uang H J. Mixed H2/H∞ fuzzy output feedback control design for nonlinear dynamic systems:an LMI approach[J], IEEE Transactions on Fuzzy Systems,2000.8(3):249-265.
120. Han Z X, Feng G, Walcott B L. et al. Dynamic output feedback controller design for fuzzy systems[J], IEEE Transactions on Systems, Man and Cybernetics, Part B, 2000.30(1):204-210.
121. Zheng F, Wang Q G, Lee T H, et al. Robust PI controller design for nonlinear systems via fuzzy modeling approach[J], IEEE Transactions on Systems. Man and Cybernetics, Part A.,2001,31(6):666-675.
122. Katayama H, Ichikawa A. H∞ control for discrete-time Takagi-Sugeno fuzzy sys-tems[J]. International Journal of Systems Science,2002,33(14):1099-1107.
123. Nguang S K, Shi P. Fuzzy output feedback control of nonlinear systems under sampled measurements [J], Automatica,2003,39(12):2169-2174.
124. Lin M L, Lo J C. An iterative solution to dynamic output stabilization and com-ments on "Dynamic output feedback controller design for fuzzy systems"[J], IEEE Transactions on Systems, Man and Cybernetics. Part B,2004,34(1):679-681.
125. Chen S S, Chang Y C, Su S F, et al. Robust static output-feedback stabilization for nonlinear discrete-time systems with time delay via fuzzy control approach[J], IEEE Transactions on Fuzzy Systems,2005,13(2):263-272.
126. Cao Y Y, Lam J, Sun Y X. Static output feedback stabilization:An ILMI ap-proach[J]. Automatica,1998,34(12):1641-1645.
127. Wu H N, Zhang H Y. Reliable mixed L2/H∞ fuzzy static output feedback control for nonlinear systems with sensor faults[J], Automatica,2005,41(11):1925-1932.
128. Lo J C, Lin M L. Robust H∞ nonlinear control via fuzzy static output feedback[J], IEEE Transactions on Circuits and Systems I:Fundamental Theory and Applica-tions,2003,50(11):1494-1502.
129. Kau S W, Lee H J, Yang C M, et al. Robust H∞ fuzzy static output feedback con-trol of T-S fuzzy systems with parametric uncertainties[J]. Fuzzy Sets and Systems. 2007,158(2):135-146.
130. Crusius C A R, Trofino A. Sufficient LMI conditions for output feedback control problems[J], IEEE Transactions on Automatic Control,1999,44(5):1053-1057.
131. Apkarian P, Hoang Duong T, Bernussou J. Continuous-time analysis, eigenstruc-ture assignment, and H2 synthesis with enhanced linear matrix inequalities (LMI) characterizations[J], IEEE Transactions on Automatic Control,2001,46(12):1941-1946.
132. Liu X, Zhang Q. Approaches to quadratic stability conditions and H∞ con-trol designs for T-S fuzzy systems[J], IEEE Transactions on Fuzzy Systems,2003, 11(6):830-839.
133. Boyd S, Ghaoui L E, Feron E, et al. Linear Matrix Inequalities in System and Control Theory[M], Philadelphia:Society for Industrial and Applied Mathematics, PA:SIAM.1994.
134. Ding B, Sun H, Yang P. Further studies on LMI-based relaxed stabilization conditions for nonlinear systems in Takagi-Sugeno's form[J], Automatica,2006, 42(3):503-508.
135. Yang B, Yu D C, Feng G, et al. Stabilisation of a class of nonlinear continuous time systems by a fuzzy control approach [J], IEE Proceedings-Control Theory and Applications,2006,153(4):427-436.
136. Wu H N, Cai K Y. H2 guaranteed cost fuzzy control design for discrete-time non-linear systems with parameter uncertainty [J], Automatica,2006,42(7):1183-1188.
137. Lee H J, Park J B, Joo Y H. Robust load-frequency control for uncertain non-linear power systems:A fuzzy logic approach[J], Information Sciences,2006, 176(23):3520-3537.
138. Ting C S. Stability analysis and design of Takagi-Sugeno fuzzy systems[J], Infor-mation Sciences,2006,176(19):2817-2845.
139. Ohtake H, Tanaka K, Wang H O. Switching fuzzy controller design based on switching Lyapunov function for a class of nonlinear systems[J], IEEE Transactions on Systems, Man and Cybernetics. Part B,2006,36(l):13-23.
140. Yu G R. Chen S H. Nonlinear flight control of a Two-Degree-of-Freedom he-licopter using Takagi-Sugeno fuzzy model[C], IEEE International Conference on Systems, Man and Cybernetics. Taiwan, China,2006,5:4354-4359.
141. Lian K Y, Su C H. Huang C S. Performance enhancement for T-S fuzzy control using neural networks[J], IEEE Transactions on Fuzzy Systems,2006,14(5):619-627.
142. Wang W J, Sun C H. A relaxed stability criterion for T-S fuzzy discrete systems[J], IEEE Transactions on Systems. Man and Cybernetics, Part B,2004,34(5):2155-2158.
143. Huang D, Nguang S K. Static output feedback controller design for fuzzy systems: An ILMI approach[J], Information Sciences,2007,177(14):3005-3015.
144. Chen B, Liu X, Tong S. Delay-dependent stability analysis and control synthe-sis of fuzzy dynamic systems with time delay[J], Fuzzy Sets and Systems,2006. 157(16):2224-2240.
145. Choi D J, Park P, Chang M S. A dynamic output-feedback variable structure controller design for uncertain fuzzy systems[C], IEEE International Conference on Systems, Man and Cybernetics.2003,1:804-809.
146. Lam J, Zhou S. Dynamic output feedback H∞ control of discrete-time fuzzy sys-tems:a fuzzy-basis-dependent Lyapunov function approach[J]. International Journal of Systems Science,2007.38(1):25-37.
147. Li J, Wang H O, Niemann D, et al. Dynamic parallel distributed compensation for Takagi-Sugeno fuzzy systems:An LMI approach[J], Information Sciences,2000, 123(3-4):201-221.
148. Tanaka K, Yamauchi K, Ohtake H, et al. Optimal dynamic output feedback de-signs for backing-up control of a vehicle with triple trailers[C], IEEE International Conference on Fuzzy Systems. Vancouver, BC, Canada,2006:2385-2391.
149. Tuan H D. Apkarian P. Narikiyo T, et al. New fuzzy control model and dynamic output feedback parallel distributed compensation[J], IEEE Transactions on Fuzzy Systems,2004,12(1):13-21.
150. Xu S, Lam J. Robust H∞ control for uncertain discrete-time-delay fuzzy sys-tems via output feedback controllers[J], IEEE Transactions on Fuzzy Systems,2005, 13(1):82-93.
151. Yoneyama J. Robust H∞ control analysis and synthesis for Takagi-Sugeno general uncertain fuzzy systems[J], Fuzzy Sets and Systems,2006,157(16):2205-2223.
152. Nguang S K, Shi P. H∞ fuzzy output feedback control design for nonlinear sys-tems:an LMI approach[J], IEEE Transactions on Fuzzy Systems,2003,11(3):331-340.
153. Wu H N, Cai K Y. H2 guaranteed cost fuzzy control for uncertain nonlinear systems via linear matrix inequalities [J], Fuzzy Sets and Systems,2004,148(3):411-429.
154. Dong J, Yang G H. Static output feedback control synthesis for linear systems with time-invariant parametric uncertainties[J], IEEE Transactions on Automatic Control, 2007,52(10):1930-1936.
155. Dong J, Yang G H. Static output feedback control synthesis for discrete-time T-S fuzzy systems[J], International Journal of Control Automation and Systems,2007, 5(3):349-354.
156. Chilali M, Gahinet P. H∞ design with pole placement constraints:an LMI ap-proach[J], IEEE Transactions on Automatic Control,1996,41(3):358-367.
157. Nguang S K, Shi P. Robust H∞ output feedback control design for fuzzy dynamic systems with quadratic D stability constraints:An LMI approach[J], Information Sciences,2006,176(15):2161-2191.
158. Wang L, Feng G. Piecewise H.x controller design of discrete time fuzzy sys-tems[J], IEEE Transactions on Systems, Man and Cybernetics, Part B,2004, 34(1):682-686.
159. Wang H O, Tanaka K. Griffin M F. An approach to fuzzy control of nonlinear systems:stability and design issues[J], IEEE Transactions on Fuzzy Systems,1996, 4(1):14-23.
160. Delmotte F, Guerra T M, Ksantini M. Continuous Takagi-Sugeno's models:re-duction of the number of LMI conditions in various fuzzy control design technics[J], IEEE Transactions on Fuzzy Systems,2007,15(3):426-438.
161. Teixeira M C M, Zak S H. Stabilizing controller design for uncertain nonlinear sys-tems using fuzzy models[J], IEEE Transactions on Fuzzy Systems,1999,7(2):133-142.
162. Chen B, Liu X, Tong S, et al. Guaranteed cost control of T-S fuzzy systems with state and input delays[J], Fuzzy Sets and Systems,2007.158(20):2251-2267.
163. Petersen I R, McFarlane D C. Optimal guaranteed cost control and filtering for uncertain linear systems[J], IEEE Transactions on Automatic Control,1994, 39(9):1971-1977.
164. Pawluszewicz E, Bartosiewicz Z. Euler' discretization and dynamic equivalence of nonlinear control systems[M], Nonlinear control. Springer Berlin/Heidelberg,2001, 2:183-191.
165. Fridman E. A descriptor system approach to nonlinear singularly perturbed optimal control problem[J], Automatica,2001.37(4):543-549.
166. Fridman E. Effects of small delays on stability of singularly perturbed systems[J], Automatica,2002,38(5):897-902.
167. Shi P, Dragan V. Asymptotic H∞ control of singularly perturbed systems with parametric uncertainties[J], IEEE Transactions on Automatic Control,1999. 44(9):1738-1742.
168. Garcia G, Daafouz J, Bernussou J. The infinite time near optimal decentralized reg-ulator problem for singularly perturbed systems:a convex optimization approach[J], Automatica,2002,38(8):1397-1406.
169. Fridman E. Robust sampled-data H∞ control of linear singularly perturbed sys-tems[J], IEEE Transactions on Automatic Control.2006.51(3):470-475.
170. Assawinchaichote W, Nguang S K, Shi P. Robust H∞ fuzzy filter design for un-certain nonlinear singularly perturbed systems with Markovian jumps:An LMI ap-proach[J]. Information Sciences,2007,177(7):1699-1714.
171. Saksena V R, Cruz J, J. Stabilization of singularly perturbed linear time-invariant systems using low-order observers[J], IEEE Transactions on Automatic Control, 1981,26(2):510-513.
172. Chen Y, Liu Y. Summary of singular perturbation modeling of multi-time scale power systems[C], Transmission and Distribution Conference and Exhibition:Asia and Pacific. Dalian, China,2005:1-1.
173. Lizarraga I, Etxebarria V. Combined PD-H∞ approach to control of flexible link manipulators using only directly measurable variables[J], Cybernetics and Systems, 2003,34(1):19-31.
174. Sandell N R. Robust stability of systems with application to singular perturba-tions[J], Automatica,1979,15(4):467-470.
175. Shao Z H, Sawan M E. Robust stability of singularly perturbed systems[J], Inter-national Journal of Control,1993,58(6):1469-1476.
176. Sen S, Datta K B. Stability bounds of singularity perturbed systems[J], IEEE Transactions on Automatic Control,1993,38(2):302-304.
177. Mustafa D, Davidson T N. Block bialternate sum and associated stability formu-lae[J], Automatica,1995,31(9):1263-1274.
178. Isidori A. H∞ control via measurement feedback for affine nonlinear systems[J], International Journal of Robust and Nonlinear Control,1994,4(4):553-574.
179. Zak S H, Maccarley C. State-feedback control of non-linear systems[J], Interna-tional Journal of Control 1986,43:1497-1514.
180. Lin W, Byrnes C I. H∞-control of discrete-time nonlinear systems[J], IEEE Trans-actions on Automatic Control,1996,41(4):494-510.
181. Boyd S, Vandenberghe L. Convex Optimization[M], Cambridge University Press, 2004.
182. Wu H N. Reliable LQ fuzzy control for nonlinear discrete-time systems via LMIs[J], IEEE Transactions on Systems, Man and Cybernetics, Part B,2004, 34(2):1270-1275.
183. Feng G. Approaches to quadratic stabilization of uncertain fuzzy dynamic sys-tems[J], IEEE Transactions on Circuits and Systems I:Fundamental Theory and Ap-plications,2001,48(6):760-769.
184. Feng G, Chen C L, Sun D, et al. H∞ controller synthesis of fuzzy dynamic systems based on piecewise Lyapunov functions and bilinear matrix inequalities[J], IEEE Transactions on Fuzzy Systems,2005.13(1):94-103.
185. Pan G L, BarShalom Y. Stabilization of jump linear Gaussian systems without mode observations[J], International Journal of Control,1996,64(4):631-661.