Input-to-state stability and stabilization of impulsive switched nonlinear systems

In this paper, the input-to-state stability and stabilization for a class of impulsive switched nonlinear systems are investigated. Two cases are considered based on whether or not subsystems are input-to-state stable (ISS). For the case that all subsystems are ISS, due to impulsive behaviors at switching instants causing the instability, the average dwell time (ADT) approach is used to obtain sufficient conditions on guaranteeing ISS of the impulsive switched nonlinear systems. While for the case that subsystems are not ISS, the nonlinear controller and switching law are designed simultaneously to stabilize the impulsive switched nonlinear systems and ensure the ISS property. At last, two numerical examples are given to illustrate the effectiveness of the results established.