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针对一类连续时间Takagi-Sugeno(T-S)模糊系统,研究了其镇定和H_∞控制器设计问题.基于模糊李亚普诺夫方法和并行分布补偿(PDC)算法,通过对隶属函数时间导数特性的进一步探究,并引入更松弛矩阵变量,给出了以线性矩阵不等式(LMI)形式表示的新的镇定条件及相应的H_∞控制器设计方法.所提方法将李亚普诺夫矩阵从系统矩阵中解耦出来,并充分考虑隶属函数时间导数的特性,为LMI问题提供了更多的自由度.数值仿真表明,新的镇定条件扩大了系统的镇定区域,降低了保守性,设计的H_∞控制器具有较小的扰动衰减度,提高了系统的H_∞性能.
For a class of continuous-time Takagi-Sugeno (TS) fuzzy systems, the stabilization and H_∞controller design problems are studied. Based on the fuzzy Lyapunov method and the parallel distributed compensation (PDC) algorithm, the time derivative properties of membership functions And introduces a more relaxed matrix variable, and presents a new stabilization condition and corresponding H_∞controller design method in the form of linear matrix inequality (LMI). The proposed method decouples the Lyapunov matrix from the system matrix And takes full account of the characteristics of time derivatives of membership functions, which provides more degrees of freedom for LMI problems.The numerical simulation shows that the new stabilization condition expands the stabilization region of the system and reduces the conservativeness. The designed H_∞controller has Smaller disturbance decay degree, improve the H_∞ performance of the system.