不确定变时滞系统的指数稳定

Exponential Stability of Uncertain Systems with Time-varying Delay

针对一类含有不确定项的时变时滞动力系统,根据李雅普诺夫第二方法,采用线性矩阵不等式(LIM)处理方法,对其指数稳定问题进行了研究。通过构造适当的李雅普诺夫函数,利用积分不等式技术,得到一个不确定时滞相关系统指数稳定的新判据,并将其转化为线性矩阵不等式的形式,从而可以很方便地利用Matlab工具箱求解得到一般动力系统指数稳定的时滞的相关最大上界,最后通过数值例子说明结果的可行性,其结果具有较小的保守性,而且在实际应用有重要意义。

Based on Lyapunov stability theory and the linear matrix inequality （ LMI ） approach, the proDlem ot exponenuai stanulty oi uncertain systems with time-varying delay is investigated. By constructing the appropriate Lyapunov functional, using integral inequality technique, a new criterion of the exponential stability is derived. It can be easily solved by Matlab toolbox. By comparing our results with others through numerical examples, it has been shown that the derived criterion is less conservative than those in the literature, and has important significance in practical application.