Stability analysis of switched systems with all subsystems unstable: A matrix polynomial approach

Abstract

This paper concentrates on the problem of continuous-time switched linear systems with all subsystems unstable under average dwell time (ADT) criteria. Inspired by the matrix polynomial approach, a new method is proposed to further lessen conservativeness and improve system performance. The new method is based on a matrix polynomial and the discretized Lyapunov function (DLF) technique. Using the matrix polynomial, the DLF is successfully established and applied to switched systems. Based on this function, convex sufficient conditions are derived, thereby ensuring the global uniform exponential stability of the system. In addition, the method can be expanded to uncertain systems. Finally, a numerical example is presented to illustrate the potential of the proposed approach.