The Analysis Of Stability And L₂Gain For Hybrid Systems

First of all, this paper improves the existing results that the desired L2-gain per-formance can not be guaranteed for switched systems with average dwell time (ADT) and should be replaced by weighted L2-gain performance. The improved results con-cern that asynchronously switched systems with ADT achieve an L2-gain performance in both continuous-time and discrete-time contexts. Our results can be readily applied into some existing literatures on weighted L2-gain analysis for switched systems with ADT.Secondly, base on above discussion, this paper presents the stability and L2-gain for nonlinear and linear switched systems with mode-dependent average dwell time.Last, this paper presents the exponential stability with Ⅱ∞performance analysis for a class of uncertain nonlinear impulsive switched systems by using the average impulsive interval (AⅡ). We also study the control synthesis for a class of uncertain nonlinear impulsive switched systems by using All with piecewise Lyapunov functions. Sufficient conditions for H∞performance and stabilization are derived under some switching signal for such systems, where not all subsystems are stable. A switched state feedback controller is designed to achieve exponential stability of such closed-loop system with the H∞performance. The efficiency of the obtained results is illustrated by a numerical example.