Stability analysis of cyclic switched linear systems: An average cycle dwell time approach

Abstract

In this paper, the stability problem of switched linear systems with a class of cyclic switching signals is investigated. Firstly, a new concept of average cycle dwell time (ACDT) is introduced to relax the conservativeness of cycle dwell time that is extensively used in the literature. In addition, the ACDT is further extended to stable cyclic switching sequence dependent average cycle dwell time (S-ACDT) and unstable cyclic switching sequence dependent average cycle dwell time (U-ACDT). Secondly, the stability criteria for cyclic switched linear (or nonlinear) systems with ACDT or both S-ACDT and U-ACDT are derived by resorting to a technique that uses multiple Lyapunov functions. Both cyclic switched linear systems and cyclic switched nonlinear systems which contain all stable subsystems or partly stable subsystems are studied. Finally, a numerical example is given to demonstrate the feasibility of the proposed techniques.