一类带有时变时滞和非线性扰动的切换系统的鲁棒指数稳定性

摘要

讨论了一类带有时变时滞和非线性扰动的切换系统的鲁棒指数稳定性问题。通过构造新的李雅普诺夫-克拉索夫斯基函数研究切换系统的稳定性，同时考虑了时变时滞对系统稳定性的影响。在系统分析过程中，采用自由权矩阵的方法，提高问题的可解性并使结果具有更小的保守性，切换策略采用平均驻留时间的方法，未知的非线性扰动采用通常的限制方法。根据 Lyapunov稳定性定理，得到了切换系统时滞依赖鲁棒指数稳定性的充分条件。该判定条件不易检验，利用 Schur补引理可以把这个条件化成等价的易于求解的线性矩阵不等式形式，从而获得该类系统鲁棒稳定性的切换控制策略。%This paper considers the robust exponential stability for switched systems with time-varying delay and nonlinear perturbations.A Lyapunov-Krasovskii function,which takes the range information of the time-varying delay into account, is proposed to analyze the stability. Furthermore,we also consider the effect of time-varying delay on the stability of switched systems. In the analysis of switched systems,free-weighting matrices is employed to improve the solvability of problems and make the result be less conservative.The switching strategy is proj ected by using average dwell time method,and nonlinear perturbations are limited to common constraint without loss generality.The sufficient condition of delay-range-dependent exponential stability for switched systems is presented by using Lyapunov stability theory.However,this condition is not easy to verify.This problem can be solved easily by transforming them into equivalent linear matrix inequalities (LMIS)using Schur complement lemma.Finally,switched law of robust exponential stability is obtained for switched systems with time-varying delay and nonlinear perturbations.