Admissible control for a class of switched and descriptor systems with impulsive effects

Switching and impulsive phenomena often appear in practical dynamical systems. The impulse at switching instants is taken into account and, in this paper, the admissible control problem of a class of switched and descriptor systems with impulsive effects is investigated. Furthermore, the descriptor matrix of each descriptor subsystem is allowed to have different rank. By designing a feedback controller and an impulsive controller, the corresponding closed-loop systems can be admissible (regular, impulsive-free and stable). The conditions for the existence of such controllers are proposed in terms of strict linear matrix inequality (LMI). An example is given to show the effectiveness of the design method in this paper.