In this paper, two new relaxed stabilization criteria for discrete-time T-S fuzzy systems are proposed. In the beginning, the operation state space is divided into several subregions, and then, the T-S fuzzy system is transformed to an equivalent switching fuzzy system corresponding to each subregion. Consequently, based on the piecewise Lyapunov function, the stabilization criteria of the switching fuzzy system are derived. The criteria have two features: 1) the behavior of the two successive states of the system is considered in the inequalities and 2) the interactions among the fuzzy subsystems in each subregion Sj are presented by one matrix Xj. Due to the above two features, the feasible solutions of the inequalities in the criteria are much easier to be found. In other words, the criteria are much more relaxed than the existing criteria proposed in other literature. The proposed conditions in the criteria and the fuzzy control design can be solved and achieved by means of linear matrix inequality tools. Two examples are given to present the superiority of the proposed criteria and the effectiveness of the fuzzy controller's design, respectively.

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Stability conditions for Tanaka-Sugeno (T-S) fuzzy discrete systems based on a single quadratic Lyapunov function or a weighting dependent Lyapunov function have been mentioned in lots of literature. The existence of a common matrix P is required in the former, and r (rules' number) positive matrices satisfying r2 Lyapunov inequalities are necessary in the latter. In this paper, the weighting dependent Lyapunov function is used again. Moreover according to the idea of the firing rule group and the distance estimation between two successive states of the system, the relaxed stability criterion of T-S fuzzy discrete system is proposed.

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