Disturbance attenuation properties of time-controlled switched systems

In this paper, we investigate the disturbance attenuation properties of tim e-controlled switched systems consisting of several linear time-invariant s ubsystems by using an average dwell time approach incorporated with a piece wise Lyapunov function. First, we show that when all subsystems are Hurwitz stable and achieve a disturbance attenuation level smaller than a positive scalar gamma (0), the switched system under an average dwell time scheme a chieves a weighted disturbance attenuation level gamma (0), and the weighte d disturbance attenuation approaches normal disturbance attenuation if the average dwell time is chosen sufficiently large. We extend this result to t he case where not all subsystems are Hurwitz stable, by showing that in add ition to the average dwell time scheme, if the total activation time of uns table subsystems is relatively small compared with that of the Hurwitz stab le subsystems, then a reasonable weighted disturbance attenuation level is guaranteed. Finally, a discussion is made on the case for which nonlinear n orm-bounded perturbations exist in the subsystems. (C) 2001 Published by El sevier Science Ltd. on behalf of The Franklin Institute.