中文摘要：

研究时变时滞切换系统的指数稳定性及相应的L2增益分析问题。构建了一类限定时滞上界和下界的特殊分段Lyapunov-Krasovskii函数,通过时滞分解方法及Jensen积分不等式与倒数凸组合相结合的技术处理了分段Lyapunov-Krasovskii函数中的积分项。更进一步,在估计泛函微分的上界过程中,一方面,未引入加权矩阵,从而涉及较少的决策变量,降低了计算复杂性;另一方面,未忽略任何有效信息,因此获得了具有更小保守性的稳定性结论。此外,利用平均驻留时间的方法给出了时变时滞切换系统的指数稳定性及L2增益的充分条件,同时也给出了切换律的设计方案。最后,将时变时滞切换系统的稳定性及L2增益分析问题归结为线性矩阵不等式的求解问题,这样便于利用Matlab工具箱求解并验证结论有效性。

英文摘要：

This article studies the problem of exponential stability and Lz gain analysis of a kind of switched systems with time-varying delay. By using delay decomposition approach and the method of combining Jensen integral ineqaulity and reciprocally convex, the integer terms in the Lyapunov- Krasovskii function that taking both the lower bound and upper bound of delay into consideration are dealt. On the one hand, because of any free weighting matrix is not introduced, which can decrease decision variables and reduce the complexity of the operation. On the other hand, the information about the time-raring delay is not ignored to estimate the upper bound of the derivation of Lyapunov-Krasovskii function. So this method can develop a less conservative stability criterion. Moreover, the sufficient conditions of exponential stability and Lz gain analysis of a kind of switched systems with time-varying delay are gained by the average dwell-time approach. In the meantime, the designing scheme of switching law is given. At last, the problem of exponential stability and I-.2 gain analysis of a kind of switched systems with time-varying delay can be solved by linear matrix inequality teehnique, which is convenient to solve and prove to be valid by the LMIs tool box of Matlab.