Stability of Switched Systems with Unstable Subsystems: A Sequence-Based Average Dwell Time Approach

This paper proposes a new sequence-based approach to resolve the stability problems found in switched systems with unstable subsystems. In existing approaches, the sequence information of switching subsystems is seldom exploited. By exploiting the sequence information, threshold values can be less restrictive and more appropriate for the situation. We study two cases in this paper: (a) all subsystems are unstable, and (b) part of the subsystems are unstable. Both continuous-time and discrete-time systems are studied, and a numerical example is given to show the advantage of our approach.