On the Stability of Hybrid Homogeneous Systems

Abstract

The hybrid system consisting of the family of subsystems with homogeneous right-hand sides and a switching law is considered. It is assumed that the zero solution of each subsystem is asymptotically stable. By the use of the Lyapunov functions method, the classes of admissible switching laws are determined under which the corresponding hybrid system is also asymptotically stable. The region of asymptotic stability of the zero solution is investigated.