中文摘要：

笔者主要研究了一类多时变时滞切换系统的指数稳定性问题。通过采用一类特殊的限定时滞的上界与下界的分段Lyapunov-Krasovskii函数,使用平均驻留时间的方法,分析了在任意切换时间下的多时变切换系统的指数稳定性以及鲁棒指数稳定性问题。首次以线性矩阵不等式的形式给出一个新的稳定性准则。由于未引进多余的加权矩阵,在估计泛函微分上界时未忽略有用信息,即充分考虑时滞上下界信息,使得所得结果具有较小保守性,同时为了获得更小保守性的结果,引入了积分不等式的放缩方法以及线性矩阵不等式方法,以及使用线性变换降低了文章计算的复杂性。结果是以线性矩阵不等式形式给出,方便利用Matlab工具箱求解矩阵不等式,并且最后的结果可以通过数值例子证明其有效性与真实性。

英文摘要：

The problem of exponential stability and robust exponential stability for switched systems with multiple time-varing delays has been considered in this paper.Based on taking both the lower bound and upper bound of delay into consideration in the chosen piecewise Lyapunov-Krasovskii function,we investigate the exponential stability by using the method of average delay time.A new delay-rang-dependent stability criteria and the robust exponential stability conditions are first derived in terms of linear matrix inqualities.Because any free weighting matrix is not introduced and some useful terms that taken into account for information of the lower and upper bounds for the time delay are not ignored to estimate the upper bound of the derivative of Lyapunov functional,these developed results enjoy much less conservative than the existing ones.Moreover,the integral inequality approach is introduced to make less conservatism,and the linear transformation is used to reduce the complexity of the operation.The result is proven to be valid by the simulation at last.