Disturbance Attenuation Properties of Time-Controlled Switched Systems

In this paper, we investigate the disturbance attenuation properties of timecontrolled switched systems consisting of several linear time-invariant subsystems by using a dwell time approach incorporated with piecewise Lyapunov functions. First, we show that when all subsystems are Hurwitz stable and achieve a disturbance attenuation level smaller than γ0, then the switched system can achieve any disturbance attenuation level larger than γ0 if the dwell time is chosen sufficiently large. This result is extended to the case where not all subsystems are Hurwitz stable, by showing that if the dwell time is chosen sufficiently large and the total activation time of unstable subsystems is relatively small compared with that of Hurwitz stable subsystems, then a desirable disturbance attenuation level is guaranteed. Finally, a discussion is made on the case for which nonlinear norm-bounded perturbations exist in the subsystems.