Stability Analysis of Switched System With All Subsystems Unstable Under Novel Average Dwell Time Criteria

This paper analyzes the stability problem of continuous-time switched systems with all subsystems unstable. With each switched system having a minimum dwell time, this paper considered that the Lyapunov function converges in the minimum dwell time and diverges beyond the minimum dwell time, respectively. Based on that, a new globally uniformly exponentially stability (GUES) result under average dwell time (ADT) method is proposed. By using a time-dependent quadratic Lyapunov function method, convex sufficient conditions for switched linear systems are derived. The resulting conditions in this paper are enforced using the sum of squares (SOS) programming. In real-world, equipment noise is unavoidable, which may result in inaccurate system matrices measurements. Therefore, it is necessary to analyze the stability of uncertain systems. Therefore, the condition for switched linear systems is extended to uncertain systems and the robust stability condition is derived. Some numerical examples are given to illustrate the advantages of our established results.