Robust Stabilization of Continuous-Time Nonlinear Switched Systems Without Stable Subsystems via Maximum Average Dwell Time

Abstract

This paper investigates the robust stabilization problem for a class of polytopic uncertain continuous-time nonlinear switched systems without stable subsystems. In order to analyze the stability of switched systems without stable subsystems, we propose a novel switching Lyapunov function. This new switching Lyapunov function has the "switching-decreasing" property at switching instant. To obtain less conservative results, we propose the switching-decreasing parameter-dependent Lyapunov function (SDPDLF) to investigate the studied switched systems. By using the SDPDLF approach and maximum average dwell time technique, a sufficient condition is obtained to guarantee the studied switched systems to be asymptotically stable. It is shown that the average dwell time should be less than a upper bound. This is different from some previous work, where the average dwell time is larger than a lower bound. Finally, a numerical example and a practical example are provided to illustrate the effectiveness of our results.