模糊时滞系统稳定条件保守性减小研究
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摘要
作为控制领域重要研究问题之一的模糊控制理论在近年来得到了广泛的关注,同时它在工程实践方面也获得了巨大的发展。众所周知,时滞现象大量存在于各种工程系统中,时滞的存在常常导致系统不稳定或性能恶化。因此,对模糊时滞控制系统的研究具有重要的理论意义与应用价值。如何进一步获得保守性更小的稳定条件一直是时滞系统研究的难点问题。本文利用线性矩阵不等式技术和积分不等式方法,针对T-S模糊时滞系统的稳定问题,研究了获得保守性更小的时滞相关稳定条件的方法。
为了研究常时滞模糊系统的稳定条件的保守性减小问题,将积分不等式引入常时滞模糊系统的稳定性分析以及保成本控制问题中,得到基于线性矩阵不等式的稳定条件。从理论上证明本文得到的保成本控制条件可以将现有保成本结果包括为其特殊情形,充分显示了积分不等式方法的优越性。为了进一步减小T-S模糊常时滞系统的稳定性条件的保守性,将增广矩阵引入Lyapunov- Krasovskii泛函,并同时构造了新的积分不等式,然后将这一方法延伸到保成本控制问题上,给出了新的求解模糊保成本控制器的线性矩阵不等式条件。对比现存的方法,本文的方法得到结果不仅具有较小的保守性,同时还具有较少的矩阵变量,从而减少了计算量。
对于具有区间变时滞的模糊系统,为了避免了现有文献所使用的缩小积分域的方法导致的保守性,针对变时滞的特点而构造了改进型积分不等式。利用改进型积分不等式获得了模糊系统时滞相关的稳定条件,并将其推广到对时滞微分没有限制的时滞相关而时滞变化率无关的情况。由于在推导过程中,没有对积分域进行缩放,因此所得结果减少了保守性。同时对增广型Lyapunov- Krasovskii泛函情况,构造了新的积分不等式。数值仿真表明本章所获得的结果较现有成果可以得到更大的时滞上界。
研究了同时具有输入时滞和状态时滞的不确定模糊时滞系统的鲁棒镇定问题,利用并行分布补偿方法设计变时滞模糊时滞系统的状态反馈控制器。通过构造了—个新的Lyapunov-Krasovskii函数,应用积分不等式技术,获得了一些全新的时滞相关鲁棒稳定性准则,得到了时滞相关镇定的控制器设计的方法。所得到的时滞相关条件较现存文献中所得到的时滞相关条件能够获得更大的时滞上界,因此具有更小的保守性。
为了减小公共Lyapunov-Krasovskii函数所带来的保守性,基于模糊Lyapunov-Krasovskii函数讨论了区间变时滞模糊时滞系统的H∞控制问题,并且隶属度函数被引入到改进型积分不等式中。由于模糊Lyapunov- Krasovskii函数和积分不等式都考虑了隶属度函数的影响,所得时滞相关条件可将基于公共Lyapunov-Krasovskii函数所得条件包含为其特殊形式,这显示了该方法的优越性,模糊时滞系统的H∞控制条件的保守性得到了进一步减小。
将改进型积分不等式方法推广到离散情形,构造了一个基于二次型项的有限和不等式,讨论了离散模糊时滞系统的时滞相关H∞控制问题。利用二次型项的有限和不等式获得了系统在无记忆控制器作用下的保守性更小的H∞稳定条件。同时采用迭代算法和参数调整法获得无记忆控制器参数。
As an important research field, fuzzy control theory has attracted considerable attention from scientists recently. It has made a great progress in practical control technology. Since time delays are frequently encountered in a variety of engineering systems and are often sources of instability and degradation of control performance in control systems, the study on fuzzy control systems with delays is important in both theory and practice. This dissertation utilizes linear matrix inequality method and integral inequality approach for various stabilization problems of T-S fuzzy systems with time delays to obtain less conservative delay-dependent criteria.
To study conservativeness reducing problem of stabilization condition of fuzzy delay system, some integral inequalities are first introduced to analyze the stability criteria of fuzzy systems with constant time delays. The existence condition for guaranteed cost control of the fuzzy systems is obtained, and it is proved theoretically to encompass an established result in the literature as a special case, which shows well the advantages of the integral inequality approach. Moreover, some augmented matrices are introduced into Lyapunov-Krasovskii functional and new integral inequalities are constructed to further reduce conservativeness in the stability for T-S fuzzy systems with time delay. The new method is extended into guaranteed cost problem, and linear matrix inequalities based criterion for obtaining guaranteed cost controller is given. Illustrative examples show that compared with the existing results, the results obtained from the integral inequality method possess less conservativeness, and it also reduces the amount of computation with less matrix variables.
For fuzzy systems with interval time-varying delays, improved integral inequalities, constructed for the time-varying issue, are employed to avoid the conservativeness caused by integral area reducing method used in the literature. The delay-dependent stability condition is obtained based on the improved integral inequalities. Moreover, the criteria is extended into the delay-dependent/rate- independent stability condition. Without any integral area reduction, some conservativeness is reduced in the obtained results. Further more, new integral inequalities are constructed for augmented Lyapunov-Krasovskii functional. An illustrative example shows that the methods of this dissertation can lead to much larger upper of delay than the existing results.
Robust control for uncertain fuzzy systems with state delay and input delay is investigated. State feedback controller for the fuzzy systems is provided via parallel distributed compensation. A new delay dependent robust stabilization criteria is obtained based on newly constructed Lyapunov-Krasovskii functional and integral inequalities. A method of designing a delay-dependent fuzzy controller based on parameter tuning is described. The numerical example shows the effectiveness of the given method.
To reduce the conservativeness exists with common Lyapunov-Krasovskii functional, fuzzy Lyapunov-Krasovskii functional is introduced to consider the delay-dependent H∞control of fuzzy systems with interval time-varying delays. Membership function is introduced into improved integral inqequlities. Since membership function is considered in fuzzy Lyapunov-Krasovskii functional and integral inequalities, some conservativeness is further reduced in stabilization condition of fuzzy delay system. The obtained results encompass the common Lyapunov-Krasovskii functional based results as a special case, which shows well the advantage of the proposed method.
The improved integral inequalities are extended into discrete-time case and finite-sum inequalities for quadratic terms are established, the delay- dependent H∞control of fuzzy discrete-time systems with state delays is analyzed. The finite-sum inequalities for quadratic terms are used in combination with memory-less state feedback to derive delay-dependent conditions that guarantee that the resulting closed-loop system has a given H∞performance. Two methods of designing memoryless controller, one based on an iterative algorithm and the other based on parameter tuning, are described.
为了研究常时滞模糊系统的稳定条件的保守性减小问题,将积分不等式引入常时滞模糊系统的稳定性分析以及保成本控制问题中,得到基于线性矩阵不等式的稳定条件。从理论上证明本文得到的保成本控制条件可以将现有保成本结果包括为其特殊情形,充分显示了积分不等式方法的优越性。为了进一步减小T-S模糊常时滞系统的稳定性条件的保守性,将增广矩阵引入Lyapunov- Krasovskii泛函,并同时构造了新的积分不等式,然后将这一方法延伸到保成本控制问题上,给出了新的求解模糊保成本控制器的线性矩阵不等式条件。对比现存的方法,本文的方法得到结果不仅具有较小的保守性,同时还具有较少的矩阵变量,从而减少了计算量。
对于具有区间变时滞的模糊系统,为了避免了现有文献所使用的缩小积分域的方法导致的保守性,针对变时滞的特点而构造了改进型积分不等式。利用改进型积分不等式获得了模糊系统时滞相关的稳定条件,并将其推广到对时滞微分没有限制的时滞相关而时滞变化率无关的情况。由于在推导过程中,没有对积分域进行缩放,因此所得结果减少了保守性。同时对增广型Lyapunov- Krasovskii泛函情况,构造了新的积分不等式。数值仿真表明本章所获得的结果较现有成果可以得到更大的时滞上界。
研究了同时具有输入时滞和状态时滞的不确定模糊时滞系统的鲁棒镇定问题,利用并行分布补偿方法设计变时滞模糊时滞系统的状态反馈控制器。通过构造了—个新的Lyapunov-Krasovskii函数,应用积分不等式技术,获得了一些全新的时滞相关鲁棒稳定性准则,得到了时滞相关镇定的控制器设计的方法。所得到的时滞相关条件较现存文献中所得到的时滞相关条件能够获得更大的时滞上界,因此具有更小的保守性。
为了减小公共Lyapunov-Krasovskii函数所带来的保守性,基于模糊Lyapunov-Krasovskii函数讨论了区间变时滞模糊时滞系统的H∞控制问题,并且隶属度函数被引入到改进型积分不等式中。由于模糊Lyapunov- Krasovskii函数和积分不等式都考虑了隶属度函数的影响,所得时滞相关条件可将基于公共Lyapunov-Krasovskii函数所得条件包含为其特殊形式,这显示了该方法的优越性,模糊时滞系统的H∞控制条件的保守性得到了进一步减小。
将改进型积分不等式方法推广到离散情形,构造了一个基于二次型项的有限和不等式,讨论了离散模糊时滞系统的时滞相关H∞控制问题。利用二次型项的有限和不等式获得了系统在无记忆控制器作用下的保守性更小的H∞稳定条件。同时采用迭代算法和参数调整法获得无记忆控制器参数。
As an important research field, fuzzy control theory has attracted considerable attention from scientists recently. It has made a great progress in practical control technology. Since time delays are frequently encountered in a variety of engineering systems and are often sources of instability and degradation of control performance in control systems, the study on fuzzy control systems with delays is important in both theory and practice. This dissertation utilizes linear matrix inequality method and integral inequality approach for various stabilization problems of T-S fuzzy systems with time delays to obtain less conservative delay-dependent criteria.
To study conservativeness reducing problem of stabilization condition of fuzzy delay system, some integral inequalities are first introduced to analyze the stability criteria of fuzzy systems with constant time delays. The existence condition for guaranteed cost control of the fuzzy systems is obtained, and it is proved theoretically to encompass an established result in the literature as a special case, which shows well the advantages of the integral inequality approach. Moreover, some augmented matrices are introduced into Lyapunov-Krasovskii functional and new integral inequalities are constructed to further reduce conservativeness in the stability for T-S fuzzy systems with time delay. The new method is extended into guaranteed cost problem, and linear matrix inequalities based criterion for obtaining guaranteed cost controller is given. Illustrative examples show that compared with the existing results, the results obtained from the integral inequality method possess less conservativeness, and it also reduces the amount of computation with less matrix variables.
For fuzzy systems with interval time-varying delays, improved integral inequalities, constructed for the time-varying issue, are employed to avoid the conservativeness caused by integral area reducing method used in the literature. The delay-dependent stability condition is obtained based on the improved integral inequalities. Moreover, the criteria is extended into the delay-dependent/rate- independent stability condition. Without any integral area reduction, some conservativeness is reduced in the obtained results. Further more, new integral inequalities are constructed for augmented Lyapunov-Krasovskii functional. An illustrative example shows that the methods of this dissertation can lead to much larger upper of delay than the existing results.
Robust control for uncertain fuzzy systems with state delay and input delay is investigated. State feedback controller for the fuzzy systems is provided via parallel distributed compensation. A new delay dependent robust stabilization criteria is obtained based on newly constructed Lyapunov-Krasovskii functional and integral inequalities. A method of designing a delay-dependent fuzzy controller based on parameter tuning is described. The numerical example shows the effectiveness of the given method.
To reduce the conservativeness exists with common Lyapunov-Krasovskii functional, fuzzy Lyapunov-Krasovskii functional is introduced to consider the delay-dependent H∞control of fuzzy systems with interval time-varying delays. Membership function is introduced into improved integral inqequlities. Since membership function is considered in fuzzy Lyapunov-Krasovskii functional and integral inequalities, some conservativeness is further reduced in stabilization condition of fuzzy delay system. The obtained results encompass the common Lyapunov-Krasovskii functional based results as a special case, which shows well the advantage of the proposed method.
The improved integral inequalities are extended into discrete-time case and finite-sum inequalities for quadratic terms are established, the delay- dependent H∞control of fuzzy discrete-time systems with state delays is analyzed. The finite-sum inequalities for quadratic terms are used in combination with memory-less state feedback to derive delay-dependent conditions that guarantee that the resulting closed-loop system has a given H∞performance. Two methods of designing memoryless controller, one based on an iterative algorithm and the other based on parameter tuning, are described.
引文
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