基于模糊Lyapunov函数对带有离散无穷分布时滞的T-S模糊系统的非PDC广义H_2控制  

Generalized H2 Non-PDC Control for T-S Fuzzy System with Infinite Distributed Delays Based on Fuzzy Lyapunov Function

作　　者：李江荣[1] 李俊民[2] 崔志明[1] 

机构地区：[1]延安大学计算机学院,陕西延安716000 [2]西安电子科技大学理学院,陕西西安710071

出　　处：《模糊系统与数学》2013年第3期11-22,共12页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(60974139);中央高校基本科研业务费专项资金项目(72103676);延安大学自然科学专项基金资助项目(YD2012-02;YD2011-09);陕西省高水平大学建设专项资金资助项目(2012SXTS07)

摘　　要：基于模糊分段非二次李雅普诺夫(Lyapunov)函数稳定性理论,对一类受外部干扰且带有离散无穷分布时滞的T-S模糊系统的广义H2稳定控制问题进行了讨论。通过设计非PDC(Non-PDC)模糊控制器,充分考虑子邻域Ωi(i=1,2,…,s)之间的转移,给出了保守性较小的使闭环系统广义H2稳定的充分性条件。控制器的设计可以通过线性矩阵不等式(LMI)方法求解得到。仿真例子验证了该方法的有效性。This paper deals with the generalized H2 control problem for a class of discrete-time Takagai- sugeno （T-S） fuzzy systems with time delays and external disturbances. The time delay is assumed to be infinitely in the discrete-time domain. Firstly, the premise variable space of the T-S fuzzy system is divided into several polyhedral regions, and then, the T-S fuzzy system is transformed to an equivalent switching fuzzy system corresponding to each subregion. Consequently, based on the extended Non-quadratic piecewise Lyapunov functions and the non parallel distributed compensation （Non-PDC） control law, two stabilization criteria with Hz performance can be established for the switching fuzzy system with infinite- distributed delays. The proposed conditions in the criteria and the Non-PDC fuzzy controllers can be obtained by solving a set of linear matrix inequalities（LMIs）. Finally, a simulation example is exploited in order to illustrate the effectiveness of the proposed design procedures.

关 键 词：切换模糊系统 H2控制 线性矩阵不等式(LMI) 无穷分布时滞 非二次Lyapunov函数 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]