Stabilization of Impulsive Switched Systems: State-Dependent Switching Approach
研究了一类非线性脉冲切换系统的全局指数稳定性问题，通过状态依赖切换律，即使所有脉冲子系统都不稳定也能实现稳定，并分析了脉冲频率对稳定性的影响。
This article investigates the problem of globally exponential stability (GES) for a class of nonlinear impulsive switched systems. By means of impulsive control theory and Lyapunov function method, some GES criteria for the addressed systems are obtained by a state-dependent switching (SDS) law. Different from the traditional SDS approach which is generally based on the framework of continuous state space, our results are presented in the framework of impulse action. On the one hand, it is shown that by virtue of SDS approach, the GES can still be achieved even all impulsive subsystems are unstable. On the other hand, it is shown that when the continuous dynamics of the subsystems are destabilizing, the impulse action may contribute to the stability as well as the SDS action if there is a lower restriction on the impulse frequency; when the continuous dynamics of the subsystems are stabilizing, under the help of SDS action, the destabilizing (disturbance) effect of impulses is allowed in the absence of frequent impulses. Two numerical examples are presented to illustrate the effectiveness of the obtained results.