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In this paper, the stability problem of discrete-time switched nonlinear systems with all subsystems unstable is investigated. The nonlinear subsystems are represented by the Takagi-Sugeno (T-S) fuzzy models. By constructing a novel piecewise multiple Lyapunov function approach, an exponential stability condition of switched T-S fuzzy systems is first established with the bounded maximum average dwell time. A numerical example is finally provided to illustrate the effectiveness of the obtained theoretical results.INDEX TERMS Discrete-time switched nonlinear systems, Takagi-Sugeno (T-S) fuzzy models, bounded maximum average dwell time (BMADT), piecewise multiple Lyapunov function (PMLF).

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