基于增广Lyapunov泛函的时变时滞T-S模糊系统稳定性分析

Stability Analysis of T-S Fuzzy Systems with Time-Varying Delay Based on Augmented Lyapunov Functional

针对含有时变时滞的T-S模糊系统进行稳定性分析。首先,利用线积分李雅普诺夫函数和增广李雅普诺夫泛函方法,构造一个包含更多有效信息的李雅普诺夫泛函,使增广向量中不仅包含了双重积分,还包括含时滞乘积项的双重积分。然后,采用一种估计精度更高的广义自由权矩阵不等式方法对泛函导数中的积分项进行界定,从而得到了保守性更小的稳定性判据。接着,对所得到的稳定性条件通过三阶矩阵不等式判定方法转化为线性矩阵不等式的形式。最后,采用两个数值算例验证所提出的稳定性判据的优势。

An analysis has been made of the stability of T-S fuzzy systems with a time-varying delay.Firstly,by using the line integral Lyapunov function as well as the augmented Lyapunov functional method,a Lyapunov functional with more effective information is constructed,so as to make it possible that the augmented vector includes not only double integrals,but also time-delay product double integrals.Secondly,a generalized free weight matrix inequality method with a higher estimation accuracy is adopted to define the integral term in the functional derivative,thus obtaining a less conservative stability criterion.Then,the stability conditions are transformed into linear matrix inequalities by the third order matrix inequalities.Finally,a verification of the advantages of the proposed stability criterion can be achieved by providing two numerical examples.