Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results

  • Lin H
  • Antsaklis P
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Abstract

During the past several years, there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems. This paper aims to briefly survey recent results in this field. First, the stability analysis for switched systems is reviewed. We focus on the stability analysis for switched linear systems under arbitrary switching, and we highlight necessary and sufficient conditions for asymptotic stability. After a brief review of the stability analysis under restricted switching and the multiple Lyapunov function theory, the switching stabilization problem is studied, and a variety of switching stabilization methods found in the literature are outlined. Then the switching stabilizability problem is investigated, that is under what condition it is possible to stabilize a switched system by properly designing switching control laws. Note that the switching stabilizability problem has been one of the most elusive problems in the switched systems literature. A necessary and sufficient condition for asymptotic stabilizability of switched linear systems is described here.

Author-supplied keywords

  • Automotive engineering
  • Control systems
  • Difference equations
  • Linear systems
  • Logic
  • Lyapunov function
  • Lyapunov methods
  • Nonlinear systems
  • Signal generators
  • Stability analysis
  • Sufficient conditions
  • Switched systems
  • arbitrary switching
  • asymptotic stability
  • control system analysis
  • control system synthesis
  • linear systems
  • multiple Lyapunov function theory
  • restricted switching
  • stability
  • stabilization
  • switched linear system stability analysis
  • switched systems
  • switching control law design
  • switching stabilization problem
  • time-varying systems

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Authors

  • H Lin

  • P J Antsaklis

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