时滞切换系统指数稳定性分析：Lyapunov-Krasovskii泛函方法

考虑由两个线性时滞子系统构成的切换系统,分析其在任意切换序列作用下保持指数稳定性的条件.分别利用二次型与逐段二次型的Lyapunov-Krasovskii泛函构造方式给出了以线性矩阵不等式所表述的稳定性判据;进而通过状态变量代换结合积分不等式技巧证明了指数衰减率对于所有切换序列一致成立,即其完全取决于系统的结构特征.最后给出了一个算例.

On Exponential Stability of Switched Systems with Delay: Lyapunov-Krasovskii Functional Approach

We consider switched dynamical systems consisting of two linear subsystems with delay.The problem is to find conditions guaranteeing exponential stability of the system for any switching sequence.Both quadratic and piecewise quadratic construction of Lyapunov-Krasovskii functional is exploited,from which the stability criteria in terms of linear matrix inequalities are derived.Furthermore,based on the state transformation combining with integral inequality technique,it is strictly verified that the exponential decay rate holds uniformly for all switching sequence,and is definitely determined by the structure of subsystems.Numerical examples are given to demonstrate the effectiveness of our results.