连续T-S模糊系统新的镇定条件和H_∞控制器设计

Novel Stabilization Condition and H_∞ Controller Design for Continuous T-S Fuzzy Systems

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.

We study the problem of stabilization and controller design for a class of continuous-time Takagi-Sugeno(T-S) fuzzy systems.On the basis of the fuzzy Lyapunov approach and parallel distributed compensation(PDC) scheme,we derive a novel stabilization condition in terms of linear matrix inequalities(LMIs) by further exploring the properties of the time derivatives of premise membership functions and introducing more slack matrix variables.We also provide a design procedure for the responding controller.The proposed approach decouples the Lyapunov matrices from the system matrices and fully considers the properties of the time derivatives of the premise membership functions,thereby providing more freedom to the LMI problems.Numeric examples demonstrate that the novel stabilization condition enlarges the stabilization regions of the system,reduces conservatism,and ensures that the designed controller has a smaller degree of disturbance attenuation,thereby improving the performance of the system.