This paper addresses the output feedback sliding-mode control (SMC) problem for discrete-time uncertain nonlinear systems through Takagi-Sugeno fuzzy dynamic models. Combining with the sliding surface, a descriptor system is constructed to characterize the sliding motion dynamics. Sufficient conditions for asymptotic stability analysis of the sliding motion are attained by the piecewise quadratic Lyapunov functions within a convex optimization setup. Two SMC design approaches are proposed to ensure the finite-time convergence of the sliding surface. Two simulation examples are presented to show the effectiveness of the proposed approaches.
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