关于T-S模糊系统稳定性的一个代数判据

引用一个特定的矩阵测度,基于M矩阵的基本性质,分析T S模糊系统的稳定性问题·结果表明:利用T S模糊系统子系统的系数矩阵构造一个判断矩阵,该判断矩阵的稳定性蕴涵着原T S模糊系统的全局稳定性·这个代数判据不同于现有的Lyapunov稳定性框架之下的分析结果·然后,根据PDC算法,给出一种基于该代数判据的模糊状态反馈控制器的设计方法,并给出闭环T S模糊系统判断矩阵稳定的一个必要条件·最后,通过一个数值算例说明如何利用该代数判据来设计模糊状态反馈控制器·

An Algebraic Stability Criterion for T-S Fuzzy Systems

Introducing a special matrix measure and based on the elementary properties of M-matrices, the stability of T-S fuzzy systems is analyzed, and shows that the stability of a judgement matrix constructed by the coefficient matrices of related subsystems implies the global stability of the T-S fuzzy systems. This algebraic stability criterion is different from the existing results which are usually obtained within the framework of Lyapunov stability. Then, according to PDC arithmetic, a controller design method with fuzzy state feedback is given using the algebraic criterion as well as a necessary condition given to the stability of the closed-loop T-S fuzzy system's judgment matrix. An example is presented to demonstrate the method.