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A Switching Law to Stabilize an Unstable Switched Linear System
  
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KeyWord:Switched system; Unstable mode; Stabilization; Switching law; Spherical covering
Author NameAffiliation
Yuhong Zhang School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China 
Weisheng Huang School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China 
Xiaosong Yang School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China
Hubei Key Laboratory of Engineering Modeling and Science Computing, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China 
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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.