L₂ Gain Analysis of Switched Systems with Average Dwell Time

抄録

In this paper, we investigate the L₂ gain properties of time-controlled switched systems consisting of several linear time-invariant subsystems by using an average dwell time approach incorporated with a piecewise Lyapunov function. We show that when all subsystems are Hurwitz stable and have the L₂ gain smaller than a positive scalar, the switched system can achieve any L₂ gain larger than such scalar if the average dwell time is chosen sufficiently large. The result is extended to the case where state jumps occur at switching points, and to a class of nonlinear switched systems by considering a Hamilton-Jacobi inequality for each subsystem.