Stability Analysis of Switched System with All Subsystems Unstable under MDADT Criteria

Abstract

In this paper, a new mode-dependent average dwell time (MDADT) stability result of discrete-time switched systems with all subsystems unstable is investigated. Combined with MDADT analysis method, we classified subsystems into two categories: switching stable subsystems and switching unstable subsystems. State divergence caused by switching unstable subsystems could be compensated by activating switching stable subsystems for a sufficiently long time. Based on the above considerations, a new globally exponentially stability result was proposed for switched systems with all subsystems unstable. In addition, the new result is a generalization of the previous method, which is more suitable for the case of more unstable subsystems. Some numerical examples are given to illustrate the advantages of our established results.