A Switching Law to Stabilize an Unstable Switched Linear System

Abstract

Stabilization of switched systems fully composed of unstable modes is of theoretical and practical significance. In this paper, we obtain some sufficient algebraic conditions for stabilizing switched linear systems with all unstable subsystems based on the theory of spherical covering and crystal point groups. Under the proposed algebraic conditions switching laws are easy to be designed to stabilize the switched systems. Some simple examples are provided to illustrate our results.