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New stability results for discrete-time switched systems: a new multiple piecewise convex Lyapunov function approach

In this paper, a new multiple Lyapunov function is proposed to obtain the improved stability conditions for discrete-time switched systems. Firstly, a multiple piecewise convex Lyapunov function (MPCLF) is introduced for a class of switched systems to obtain the stability result under the mode-dependent average dwell time with tighter bounds. It should be pointed out that the designed MPCLF carries the future value of the system state. Then, a simulation result is provided to show the superiority of our theoretic results.