In this paper, we propose a stable fuzzy model predictive controller based on extended-fuzzy Lyapunov function. The main idea of the proposed approach is to design a free control variable and a non-parallel distributed compensation control law in such a way that an extended-fuzzy Lyapunov function is constructed with minimizing the upper bound of the infinite horizon objective function in the fuzzy model predictive control. Therefore, the predictive controller can guarantee both the stability

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... the closed-loop fuzzy model predictive control system and input constraints while obtaining the optimal transient performance. It is shown that the controller is obtained by solving a set of linear matrix inequalities. The extended-fuzzy Lyapunov function reduces the conservatism of common Lyapunov function and fuzzy Lyapunov function, and it also enlarges the feasible area of the predictive controller. Moreover, appropriate slack and collection matrices are used in all linear matrix inequalities, which can further reduce the conservatism. The simulations on a numerical example and a nonlinear boiler-turbine coordinated system demonstrate the advantage and effectiveness of the proposed approach. Index Terms-TS fuzzy model, model predictive control, extended-fuzzy Lyapunov function, slack and collection matrices.