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The stability problem of discrete-time switched systems with unstable modes is concerned under two novel switching strategies, i.e., limit inferior and superior &#x03A6;-dependent average dwell time switchings. Some improved stability criteria of discrete-time switched systems with unstable modes are obtained by combining a multiple Lyapunov function method with two strategies proposed, where limit inferior and superior switchings are applied to deal with stable and unstable modes, respectively. Especially, we also give stability conditions of discrete-time switched systems comprising stable modes. It is shown that these conditions with tighter bounds of average dwell time (ADT) and mode-dependent ADT cover some existing ones. Finally, two illustrated numerical examples are presented to show the effectiveness of the obtained theoretical results.

A Limit Φ-Dependent ADT Technique for Stability Analysis of Discrete-Time Switched Systems With Unstable Modes