Abstract
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.
