This brief is concerned with the stability problem for a class of discrete-time switched systems with unstable subsystems. By constructing a quasi-time-dependent Lyapunov function, stability analysis criterion for nonlinear switched systems is developed under a designed switching rule in which the fast and slow switching techniques are adopted for unstable and stable subsystems, respectively. Then, stability criteria for linear switched systems are presented. It is shown that the obtained results are more general and less conservative than existing ones. Some comparative simulations are provided to demonstrate the effectiveness of the proposed method.
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