Stabilization of switched linear systems via admissible edge-dependent switching signals

Abstract

This paper proposes and studies the concept of admissible edge-dependent average dwell time (AED-ADT) which characterizes a kind of new switching signals for switched systems. The switching behavior of the proposed switching signal is denoted by a directed graph, where each admissible transition edge (ATE) signifies a switching from one subsystem to another. New stability criteria for switched systems with AED-ADT switching are then derived. The choices of transition weights of ATEs make the proposed AED-ADT switching more general than mode-dependent average dwell time (MDADT) switching. Stabilization conditions for switched linear systems are also established by designing state-feedback switching controller whose gain matrices can be obtained by solving linear matrix inequalities. The effectiveness of the proposed approaches is demonstrated by a numerical example.