Periodic Stabilization of Continuous-Time Multi-Module Impulsive Switched Linear Systems

This paper mainly investigates periodic stabilization issue for a class of multi-module impulsive switched linear systems. It is proven that the considered system is exponentially stabilizable if there exists a periodic control Lyapunov function whose value decreases periodically rather than at each time instant. A Lyapunov converse theorem is also presented. In particular, a constructive method is used to determine stabilizable impulsive switching law. Moreover, the relaxed set is introduced to reduce the computational complexity, and relaxed versions of Lyapunov theorem and its converse theorem are established. Finally, a numerical example is provided to illustrate the effectiveness of the approach.