基于T-S模型的非线性时滞系统的鲁棒控制与分析
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摘要
非线性时滞系统的稳定分析与综合作为控制理论研究的热点,长期以来备受关注。T-S模糊模型方法因其自身的局部线性逼近特性,成为近些年来研究非线性时滞系统综合控制的一种重要方法。本文即是通过建立系统的T-S模糊模型,结合L函数方法和线性矩阵不等式(LMI)技术,研究了非线性时滞系统的稳定性、鲁棒模糊控制及H∞性能,主要内容及成果体现在以下几个方面：
1)从实际应用的角度设定时变时滞的下界不严格为零,研究了一类带有非线性扰动的变区间连续时滞系统的稳定性。通过构造一类全新的带调节参数的L-K泛函,以线性矩阵不等式的形式,给出了全新的带调节参数的时滞相关型稳定性判据。并经数值仿真,验证了结论较小的保守性。
2)将线性时滞系统控制中较完善的广义模型变换结合Moon不等式的处理方法推广到T-S模糊时滞系统,研究了一类不确定连续复合时滞系统的鲁棒控制。基于改进的带调节参数的L-K泛函,以LMI的形式,给出了全新的带调节参数的时滞相关型鲁棒镇定的充分条件及鲁棒状态反馈控制器的形式。在保证闭环稳定的基础上,可通过改变调节参数的值,增大时滞的范围,实现对控制器的间接调节。通过仿真实例,方法的有效性得以验证。
3)在研究不确定连续复合时滞系统鲁棒控制的基础上,继续讨论了一类带有外界扰动的不确定复合时滞系统的鲁棒H∞控制,以LMI的形式,给出了全新的带调节参数的时滞相关型鲁棒H。镇定的充分条件及鲁棒H∞状态反馈控制器的形式。在保证闭环稳定的基础上,可通过改变调节参数的值,增大时滞的变化范围,减小系统的H∞指标,实现对控制器的间接调节。通过仿真实例,验证了所得结论的有效性。
4)将连续时滞系统稳定控制研究中采用的技术合理应用于离散系统,研究了一类不确定离散复合时滞系统的鲁棒控制。通过引入前向差分变量y(k)对系统做变换,并借助积分与求和的关系,构造了一类充分利用时滞信息的新型的带调节参数的离散型L-K泛函,以LMI的形式,给出了全新的带调节参数的时滞相关型鲁棒镇定的充分条件及鲁棒状态反馈控制器的形式。在保证闭环稳定的基础上,可通过改变调节参数的值实现了对控制器的间接调节。所得结论通过仿真实例,验证了有效性。
As the focus of control theory, the stability analysis and synthesis of nonlinear time-delay system have long been attached much importance. In recent years, T-S fuzzy model method for its own local linear approximation characteristics that have become an important method to study nonlinear time-delay system.Through the establishment of the T-S fuzzy model of the system, combined with the L function method and linear matrix inequalities technology, this article study the stability, robust fuzzy control and H∞performance of nonlinear time-delay systems, the main content and the results are embodied in the following aspects:
1) From the perspective of practical application, this article sets time-varying delay the lower bound are not strictly zero, and study a class of interval time-varying delay system with nonlinear perturbation. By constructing a new kind of L-K functional with adjustable parameter, a new delay-dependent stability criteria with adjustable parameters are proposed via LMI approach. Some numerical examples have shown that the obtained results are less conservative.
2) A combination of descriptor model transformation approach and Moon s inequality technique which is effective method to deal with the linear time-varying delay systems are extended to the T-S fuzzy time-varying delay systems,and study for a kind of uncertain continuous composite robust control of time-delay systems. Based on improved L-K functional with adjustable parameters, in the form of LMI, some new containing adjustable parameter of delay-dependent sufficient conditions for the robust stabilization are given, and the robust state-feedback controller is designed. On the basis of the closed-loop systems stable, the range of the time-delay can be widened and the indirect regulation on the controller can be realized by changing adjustable parameters. Through simulation examples, the effectiveness of the method is verified.
3) Based on the results of uncertain systems with composite time-delay, H∞robust control problem is solved for the system with a disturbance outside,via LMI approach, a new containing adjustable parameters of delay-dependent robust stabilization of H∞sufficient conditions is given, and H∞robust state-feedback controller is designed. On the basis of the closed-loop systems stable, the range of the time-delay can be widened, the system H∞performance index can be reduced and the indirect regulation on the controller can be realized by changing adjustable parameters.The simulation example verify the effectiveness of the conclusion obtained.
4) The technology used in the continuous delay-system stability control reasonably is applied to the research about robust control of a class of uncertain discrete system with composite time-delay. Using the forward difference function y(k) of the system to do the transformation, and with the help of integral and summation relationship,constructing a kind of new discrete L functional with adjustable parameters, that fully contains delay informations,in the form of LMI, some new containing adjustable parameter of delay-dependent sufficient conditions for the robust stabilization are given, and the robust state-feedback controller is designed.On the basis of the closed-loop systems stable, the indirect regulation on the controller can be realized by changing adjustable parameters. Through simulation examples, the effectiveness of the method is verified.
1)从实际应用的角度设定时变时滞的下界不严格为零,研究了一类带有非线性扰动的变区间连续时滞系统的稳定性。通过构造一类全新的带调节参数的L-K泛函,以线性矩阵不等式的形式,给出了全新的带调节参数的时滞相关型稳定性判据。并经数值仿真,验证了结论较小的保守性。
2)将线性时滞系统控制中较完善的广义模型变换结合Moon不等式的处理方法推广到T-S模糊时滞系统,研究了一类不确定连续复合时滞系统的鲁棒控制。基于改进的带调节参数的L-K泛函,以LMI的形式,给出了全新的带调节参数的时滞相关型鲁棒镇定的充分条件及鲁棒状态反馈控制器的形式。在保证闭环稳定的基础上,可通过改变调节参数的值,增大时滞的范围,实现对控制器的间接调节。通过仿真实例,方法的有效性得以验证。
3)在研究不确定连续复合时滞系统鲁棒控制的基础上,继续讨论了一类带有外界扰动的不确定复合时滞系统的鲁棒H∞控制,以LMI的形式,给出了全新的带调节参数的时滞相关型鲁棒H。镇定的充分条件及鲁棒H∞状态反馈控制器的形式。在保证闭环稳定的基础上,可通过改变调节参数的值,增大时滞的变化范围,减小系统的H∞指标,实现对控制器的间接调节。通过仿真实例,验证了所得结论的有效性。
4)将连续时滞系统稳定控制研究中采用的技术合理应用于离散系统,研究了一类不确定离散复合时滞系统的鲁棒控制。通过引入前向差分变量y(k)对系统做变换,并借助积分与求和的关系,构造了一类充分利用时滞信息的新型的带调节参数的离散型L-K泛函,以LMI的形式,给出了全新的带调节参数的时滞相关型鲁棒镇定的充分条件及鲁棒状态反馈控制器的形式。在保证闭环稳定的基础上,可通过改变调节参数的值实现了对控制器的间接调节。所得结论通过仿真实例,验证了有效性。
As the focus of control theory, the stability analysis and synthesis of nonlinear time-delay system have long been attached much importance. In recent years, T-S fuzzy model method for its own local linear approximation characteristics that have become an important method to study nonlinear time-delay system.Through the establishment of the T-S fuzzy model of the system, combined with the L function method and linear matrix inequalities technology, this article study the stability, robust fuzzy control and H∞performance of nonlinear time-delay systems, the main content and the results are embodied in the following aspects:
1) From the perspective of practical application, this article sets time-varying delay the lower bound are not strictly zero, and study a class of interval time-varying delay system with nonlinear perturbation. By constructing a new kind of L-K functional with adjustable parameter, a new delay-dependent stability criteria with adjustable parameters are proposed via LMI approach. Some numerical examples have shown that the obtained results are less conservative.
2) A combination of descriptor model transformation approach and Moon s inequality technique which is effective method to deal with the linear time-varying delay systems are extended to the T-S fuzzy time-varying delay systems,and study for a kind of uncertain continuous composite robust control of time-delay systems. Based on improved L-K functional with adjustable parameters, in the form of LMI, some new containing adjustable parameter of delay-dependent sufficient conditions for the robust stabilization are given, and the robust state-feedback controller is designed. On the basis of the closed-loop systems stable, the range of the time-delay can be widened and the indirect regulation on the controller can be realized by changing adjustable parameters. Through simulation examples, the effectiveness of the method is verified.
3) Based on the results of uncertain systems with composite time-delay, H∞robust control problem is solved for the system with a disturbance outside,via LMI approach, a new containing adjustable parameters of delay-dependent robust stabilization of H∞sufficient conditions is given, and H∞robust state-feedback controller is designed. On the basis of the closed-loop systems stable, the range of the time-delay can be widened, the system H∞performance index can be reduced and the indirect regulation on the controller can be realized by changing adjustable parameters.The simulation example verify the effectiveness of the conclusion obtained.
4) The technology used in the continuous delay-system stability control reasonably is applied to the research about robust control of a class of uncertain discrete system with composite time-delay. Using the forward difference function y(k) of the system to do the transformation, and with the help of integral and summation relationship,constructing a kind of new discrete L functional with adjustable parameters, that fully contains delay informations,in the form of LMI, some new containing adjustable parameter of delay-dependent sufficient conditions for the robust stabilization are given, and the robust state-feedback controller is designed.On the basis of the closed-loop systems stable, the indirect regulation on the controller can be realized by changing adjustable parameters. Through simulation examples, the effectiveness of the method is verified.
引文
[1]胡寿松.自动控制原理[M].北京：国防工业出版社,1994.
[2]单冬. 模糊控制原理及应用[M]. 北京：中国铁道出版社,1995.
[3]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.
[4]Takagi T,Sugeno M. Fuzzy identification of systems and its applications to modeling and control[J]. IEEE Trans.Syst.,Man,Cybern,1985,15(1):116-132.
[5]谭文等. 混沌系统的模糊神经网络控制理论与方法[M].北京：科学出版社,2008.
[6]王立新. 自适应模糊系统与控制：设计与稳定性分析[M].北京：国防工业出版社,1995.
[7]Tian E G, Peng C. Delay-dependent stability analysis and synthesis of uncertain T-S fuzzy systems with time-varying delay[J]. Fuzzy Sets and Systems,2006,157:544-559.
[8]陈兵,周玉成.T-S模糊时滞模型的时滞相关稳定性分析和镇定[J].控制与决策,2004,19(9)：1022-1026.
[9]殷培强,俞立,郑科. 基于T-S模型的非线性时滞系统非脆弱保性能模糊控制[J].控制理论与应用,2008,25(1)：75-80.
[10]王树彬,王执铨. 一类模糊时滞系统的非脆弱H∞保成本鲁棒控制[J].系统工程与电子技术,2009,31(12)：2938-2941.
[11]宋晓娜,徐胜元,沈浩. 不确定T-S模糊变时滞系统的时滞依赖无源输出反馈控制[J].南京理工大学学报,2011,35(1)：6-10.
[12]邓燕妮,桂卫华,谢永芳,等. 不确定性时滞系统时滞相关鲁棒镇定[J].武汉理工大学学报(交通科学与工程版),2008,32(3)：503-506.
[13]Fang C H, Liu Y S,Kan S W,et al. A new LMI-based approach to relaxed quadratic stabilization of T-S fuzzy control systems[J]. IEEE Trans.On Fuzzy Sys,2006,14(3): 386-397.
[14]Liu X D, Zhang Q L. Approaches to qundratie stability conditions and H∞control designs for T-S fuzzy systems[J]. IEEE Trans.Fuzzy System,2003,11(6):830-839.
[15]Jeung E T, Oh DoC, Park H B. Delay-dependent control for time-delayed T-S fuzzy systems using descriptor representation[J]. International Journal of Control, Automation and Systems 2004,2 (2):182-188.
[16]Feng G. Stability analysis of discrete time fuzzy dynamic systems based on piecewise Lyapunov functions [J]. IEEE Transactions on fuzzy systems2004,12 (1):22-28.
[17]Zhang H, Li C G, Liao X F. Stablity analysis and H∞ controller design of fuzzy large-scale systems dasedon piecewise Lyapunov functions[J]. IEEE Trans. On Systems Man and Cybernetics Part B-Cybemetics,2006,36(3):685-698.
[18]张果,李俊明. 基于模糊L-K函数的模糊系统的鲁棒H∞控制[J].系统工程与电子技术,2009,31(2)：424-427.
[19]Rhee B J, Won S. A new fuzzy Lyapunov functions approach for a Takagi-Sugeno fuzzy control system design[J]. Fuzzy Sets And Systems,2006,157(9):1211-1228.
[20]俞立. 鲁棒控制一线性矩阵不等式处理方法[M].北京：清华大学出版社,2002.
[21]褚健等. 鲁棒控制理论及应用[M].北京：清华大学出版杜,2000.
[21]关心平,陈彩莲,龙承恩. 不确定离散时滞系统的动态输出反馈鲁棒保性能控制[J].控制理论与应用,2003,20:199-205.
[22]王仁民,潘俊涛,王后能,等. 时滞不确定T-S模糊系统的鲁棒控制[J].华中科技大学学报(自然科学版),2008,36(8)：45-48.
[23]王建军,谭波,毛北行. 一类时滞离散模糊系统的H∞性能分析[J]. 河南工程学院学报(自然科学版),2011,23(1)：75-77.
[24]陈学敏,张国山. 具有输入与状态时滞的非线性系统的模糊保性能控制[J]. 辽宁工学院学报,2006,26(1)：34-39.
[25]王刻奇,杨智. 不确定离散时滞系统的时滞相关保性能控制[J]. 信息与控制,2010,36(3)：373-378.
[27]陈珺,刘飞. 离散模糊时滞系统的鲁棒H∞非脆弱控制[J].系统工程与电子技术,2010,32(1)：126-132.
[28]蔡俊伟,胡寿松. 不确定时滞系统模糊静态输出反馈保性能可靠控制[J].系统工程与电子技术,2009,31(4)：887-891.
[29]GuKQ, Kharitonov, VL, Chen J. Stability of time-delay systems[C]. Boston Birkhauser,2003.
[30]Park P. A delay-dependent stability criterion for systems with uncertain time-invariant delays[J]. IEEE Transactions on Automat Control,1999,44(4):876-877.
[3l]LiC G， Wang H J, Liao X F. Delay-dependent robust stability of uncertain fuzzy systems with time-varying delays[J]. IEE Proceedings:Control Theory and Applications,2004. 151 (4):417-421.
[32]He Y, Wu M, She J H. Liu G P. Delayed-dependent robust stability criteria for uncertain neutral systems with mixed delays[J]. Systems and Control Letters,2004,51 (1): 57-65.
[33]Fridman E, Shake U. An Improved Stabilization Method for Linear Time-Delay Systems[J]. IEEE Transactions on Automat Control,2002,47 (11):1931-1937.
[34]李伯忍,胥布工. 具有非线性扰动的线性多时变时滞系统的鲁棒稳定性[J].系统科学与数学,2010,30(7)：887-894.
[35]Liu X G, Martin R R, wu M, et al. Delayed-dependent robust stabilisation of discrete-time systems with time-varying delay[J]. IEEP roeeedings:Control Theory and Aplieations, 2006,153(6):689-702.
[36]Zhang X M. Wu M, She J H, He Y. Delay-dependent stabilization of linear systems with time-varying stateand input delays [J]. Automatica.2005, 41 (8):1405-1412.
[37]何率天. 基于T-S模型的非线性时滞系统的分析与综合[D]. 硕士学位论文, 南京：东南大学2008.
[38]Xu S, Lam J. Improved delay-dependent stability criteria for time-delay systems[J]. IEEE Transactions on Automatic Control,2005,50(3):384-387.
[39]Moon Y, Park P, Kwon W. Robust stabilization of uncertain input-delayed systems using reduction method[J]. Automatica,2001,37:307-312.
[40]He Y, Wu M, Liu G P, et al. Output feedback stabilization for a discrete-time system with a time-varying delay[J]. IEEE Transactions on Automatic Control,2008,53 (10): 2372-2377.
[41]Gao H J, Chen T W. New results on stability of discrete time systems with time-varying state delay[J]. IEEE Transactions on Automatic Conrol,2007,52 (2):328-334.
[42]Lien C H, Yh K W, Chen W D, et al. Stability criteria for uncertain Takagi-Sugeno fuzzy systems with interval time-varying delay [J]. IET Control Theory AppL,2007,1(3): 764-769.
[43]苏亚坤,陈兵,张嗣瀛,等.T-S模糊时滞系统的时滞相关镇定[J].控制与决策,2009,24(6)：921-926.
[44]李丽. 非线性模糊时滞系统的鲁棒控制研究[D].博士学位论文, 大连：大连理工大学,2008.
[45]Lee H J, Park J B, Joo Y H. Robust control for uncertain Takagi-Sugeno fuzzy systems withtime-varying input delay[J]. ASME J Dyn Syst Meas Control,2005,127:302-306.
[46]Lien C H, Yu K W. Robust control for Takagi-Sugeno fuzzy systems with time-varying state and input delays[J]. Chsos, Solitons and Fractals,2008,35(5):1003-1008.
[47]Lin C, Wang Q G, Lee T H. Delay-dependent LMI conditions for stability and stabilization of T-S systems with bounded time-delay[J]. Fuzzy Sets and Systems,2006, 157:1229-1247.
[48]Moon Y S. Delay-dependent robust stabilization of uncertain state-delayed systems[J]. Int J Control,2001,74(4):1447-1455.
[49]Lee Y S， Moon Y S, Park P. Delay-dependent robust H∞ control for uncertain systems with state-delay[J]. Automatica,2004,40 (1):65-72.
[50]张蕾,刘贺平,廖福成. 改进的时变时滞不确定离散系统的鲁棒稳定性分析[J]. 控制工程,2010,17(6)： 755-758.
[51]王刻奇,杨智. 一类不确定离散时滞系统鲁棒镇定的时滞相关研究[J].科协论坛,2009(8)：102-103.
[52]汤红吉,张小美,陈树中. 一类不确定离散时滞系统的鲁棒状态反馈控制[J].华东师范大学学报(自然科学版),2005,12：97-102.
[53]张松涛,任光. 离散T-S模糊系统的稳定性分析与系统化设计[J]. 中国电机工程学报,2006,26(7)：113-11.
[54]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.
[55]刘俊,金朝永,肖元. 离散T-S模糊控制系统的稳定性研究[J].广东工业大学学报,2010,27(3)：22-26.
[56]刘亚 胡寿松. 一类离散不确定时滞系统的鲁棒模糊控制[J]. 南京理工大学学报,2004,28(2)：123-127.
[57]陈志盛,孙克辉,张泰山,等.基于LMI的不确定离散模糊时滞系统鲁棒控制[J].控制与决策,2006,21(3)：352-360.
[58]苏亚坤,陈兵,王仿桐.T-S非线性时滞系统的镇定研究[J]. 三峡大学大学学报(自然科学版),2009,31(5)：99-104.
[2]单冬. 模糊控制原理及应用[M]. 北京：中国铁道出版社,1995.
[3]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.
[4]Takagi T,Sugeno M. Fuzzy identification of systems and its applications to modeling and control[J]. IEEE Trans.Syst.,Man,Cybern,1985,15(1):116-132.
[5]谭文等. 混沌系统的模糊神经网络控制理论与方法[M].北京：科学出版社,2008.
[6]王立新. 自适应模糊系统与控制：设计与稳定性分析[M].北京：国防工业出版社,1995.
[7]Tian E G, Peng C. Delay-dependent stability analysis and synthesis of uncertain T-S fuzzy systems with time-varying delay[J]. Fuzzy Sets and Systems,2006,157:544-559.
[8]陈兵,周玉成.T-S模糊时滞模型的时滞相关稳定性分析和镇定[J].控制与决策,2004,19(9)：1022-1026.
[9]殷培强,俞立,郑科. 基于T-S模型的非线性时滞系统非脆弱保性能模糊控制[J].控制理论与应用,2008,25(1)：75-80.
[10]王树彬,王执铨. 一类模糊时滞系统的非脆弱H∞保成本鲁棒控制[J].系统工程与电子技术,2009,31(12)：2938-2941.
[11]宋晓娜,徐胜元,沈浩. 不确定T-S模糊变时滞系统的时滞依赖无源输出反馈控制[J].南京理工大学学报,2011,35(1)：6-10.
[12]邓燕妮,桂卫华,谢永芳,等. 不确定性时滞系统时滞相关鲁棒镇定[J].武汉理工大学学报(交通科学与工程版),2008,32(3)：503-506.
[13]Fang C H, Liu Y S,Kan S W,et al. A new LMI-based approach to relaxed quadratic stabilization of T-S fuzzy control systems[J]. IEEE Trans.On Fuzzy Sys,2006,14(3): 386-397.
[14]Liu X D, Zhang Q L. Approaches to qundratie stability conditions and H∞control designs for T-S fuzzy systems[J]. IEEE Trans.Fuzzy System,2003,11(6):830-839.
[15]Jeung E T, Oh DoC, Park H B. Delay-dependent control for time-delayed T-S fuzzy systems using descriptor representation[J]. International Journal of Control, Automation and Systems 2004,2 (2):182-188.
[16]Feng G. Stability analysis of discrete time fuzzy dynamic systems based on piecewise Lyapunov functions [J]. IEEE Transactions on fuzzy systems2004,12 (1):22-28.
[17]Zhang H, Li C G, Liao X F. Stablity analysis and H∞ controller design of fuzzy large-scale systems dasedon piecewise Lyapunov functions[J]. IEEE Trans. On Systems Man and Cybernetics Part B-Cybemetics,2006,36(3):685-698.
[18]张果,李俊明. 基于模糊L-K函数的模糊系统的鲁棒H∞控制[J].系统工程与电子技术,2009,31(2)：424-427.
[19]Rhee B J, Won S. A new fuzzy Lyapunov functions approach for a Takagi-Sugeno fuzzy control system design[J]. Fuzzy Sets And Systems,2006,157(9):1211-1228.
[20]俞立. 鲁棒控制一线性矩阵不等式处理方法[M].北京：清华大学出版社,2002.
[21]褚健等. 鲁棒控制理论及应用[M].北京：清华大学出版杜,2000.
[21]关心平,陈彩莲,龙承恩. 不确定离散时滞系统的动态输出反馈鲁棒保性能控制[J].控制理论与应用,2003,20:199-205.
[22]王仁民,潘俊涛,王后能,等. 时滞不确定T-S模糊系统的鲁棒控制[J].华中科技大学学报(自然科学版),2008,36(8)：45-48.
[23]王建军,谭波,毛北行. 一类时滞离散模糊系统的H∞性能分析[J]. 河南工程学院学报(自然科学版),2011,23(1)：75-77.
[24]陈学敏,张国山. 具有输入与状态时滞的非线性系统的模糊保性能控制[J]. 辽宁工学院学报,2006,26(1)：34-39.
[25]王刻奇,杨智. 不确定离散时滞系统的时滞相关保性能控制[J]. 信息与控制,2010,36(3)：373-378.
[27]陈珺,刘飞. 离散模糊时滞系统的鲁棒H∞非脆弱控制[J].系统工程与电子技术,2010,32(1)：126-132.
[28]蔡俊伟,胡寿松. 不确定时滞系统模糊静态输出反馈保性能可靠控制[J].系统工程与电子技术,2009,31(4)：887-891.
[29]GuKQ, Kharitonov, VL, Chen J. Stability of time-delay systems[C]. Boston Birkhauser,2003.
[30]Park P. A delay-dependent stability criterion for systems with uncertain time-invariant delays[J]. IEEE Transactions on Automat Control,1999,44(4):876-877.
[3l]LiC G， Wang H J, Liao X F. Delay-dependent robust stability of uncertain fuzzy systems with time-varying delays[J]. IEE Proceedings:Control Theory and Applications,2004. 151 (4):417-421.
[32]He Y, Wu M, She J H. Liu G P. Delayed-dependent robust stability criteria for uncertain neutral systems with mixed delays[J]. Systems and Control Letters,2004,51 (1): 57-65.
[33]Fridman E, Shake U. An Improved Stabilization Method for Linear Time-Delay Systems[J]. IEEE Transactions on Automat Control,2002,47 (11):1931-1937.
[34]李伯忍,胥布工. 具有非线性扰动的线性多时变时滞系统的鲁棒稳定性[J].系统科学与数学,2010,30(7)：887-894.
[35]Liu X G, Martin R R, wu M, et al. Delayed-dependent robust stabilisation of discrete-time systems with time-varying delay[J]. IEEP roeeedings:Control Theory and Aplieations, 2006,153(6):689-702.
[36]Zhang X M. Wu M, She J H, He Y. Delay-dependent stabilization of linear systems with time-varying stateand input delays [J]. Automatica.2005, 41 (8):1405-1412.
[37]何率天. 基于T-S模型的非线性时滞系统的分析与综合[D]. 硕士学位论文, 南京：东南大学2008.
[38]Xu S, Lam J. Improved delay-dependent stability criteria for time-delay systems[J]. IEEE Transactions on Automatic Control,2005,50(3):384-387.
[39]Moon Y, Park P, Kwon W. Robust stabilization of uncertain input-delayed systems using reduction method[J]. Automatica,2001,37:307-312.
[40]He Y, Wu M, Liu G P, et al. Output feedback stabilization for a discrete-time system with a time-varying delay[J]. IEEE Transactions on Automatic Control,2008,53 (10): 2372-2377.
[41]Gao H J, Chen T W. New results on stability of discrete time systems with time-varying state delay[J]. IEEE Transactions on Automatic Conrol,2007,52 (2):328-334.
[42]Lien C H, Yh K W, Chen W D, et al. Stability criteria for uncertain Takagi-Sugeno fuzzy systems with interval time-varying delay [J]. IET Control Theory AppL,2007,1(3): 764-769.
[43]苏亚坤,陈兵,张嗣瀛,等.T-S模糊时滞系统的时滞相关镇定[J].控制与决策,2009,24(6)：921-926.
[44]李丽. 非线性模糊时滞系统的鲁棒控制研究[D].博士学位论文, 大连：大连理工大学,2008.
[45]Lee H J, Park J B, Joo Y H. Robust control for uncertain Takagi-Sugeno fuzzy systems withtime-varying input delay[J]. ASME J Dyn Syst Meas Control,2005,127:302-306.
[46]Lien C H, Yu K W. Robust control for Takagi-Sugeno fuzzy systems with time-varying state and input delays[J]. Chsos, Solitons and Fractals,2008,35(5):1003-1008.
[47]Lin C, Wang Q G, Lee T H. Delay-dependent LMI conditions for stability and stabilization of T-S systems with bounded time-delay[J]. Fuzzy Sets and Systems,2006, 157:1229-1247.
[48]Moon Y S. Delay-dependent robust stabilization of uncertain state-delayed systems[J]. Int J Control,2001,74(4):1447-1455.
[49]Lee Y S， Moon Y S, Park P. Delay-dependent robust H∞ control for uncertain systems with state-delay[J]. Automatica,2004,40 (1):65-72.
[50]张蕾,刘贺平,廖福成. 改进的时变时滞不确定离散系统的鲁棒稳定性分析[J]. 控制工程,2010,17(6)： 755-758.
[51]王刻奇,杨智. 一类不确定离散时滞系统鲁棒镇定的时滞相关研究[J].科协论坛,2009(8)：102-103.
[52]汤红吉,张小美,陈树中. 一类不确定离散时滞系统的鲁棒状态反馈控制[J].华东师范大学学报(自然科学版),2005,12：97-102.
[53]张松涛,任光. 离散T-S模糊系统的稳定性分析与系统化设计[J]. 中国电机工程学报,2006,26(7)：113-11.
[54]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.
[55]刘俊,金朝永,肖元. 离散T-S模糊控制系统的稳定性研究[J].广东工业大学学报,2010,27(3)：22-26.
[56]刘亚 胡寿松. 一类离散不确定时滞系统的鲁棒模糊控制[J]. 南京理工大学学报,2004,28(2)：123-127.
[57]陈志盛,孙克辉,张泰山,等.基于LMI的不确定离散模糊时滞系统鲁棒控制[J].控制与决策,2006,21(3)：352-360.
[58]苏亚坤,陈兵,王仿桐.T-S非线性时滞系统的镇定研究[J]. 三峡大学大学学报(自然科学版),2009,31(5)：99-104.