Stability analysis and L2-gain of switched delay systems with stable and unstable subsystems

In this paper, problems of stability and L₂-gain for switched systems with time-varying delay and disturbance input are studied. Some subsystems can be unstable. By using an average dwell time approach incorporated with a piece-wise Lyapunov functional, sufficient conditions for exponential stability and weighted L₂-gain of such systems, where not all subsystems are stable, are obtained in the form of linear matrix inequalities (LMIs). It is shown that if the total activation time of stable subsystems is to some extent more than that of unstable subsystems, the exponential stability and weighted L₂-gain of the whole systems are guaranteed under an average dwell time scheme.