Stabilization Analysis for Discrete-time T-S Fuzzy Systems Based on the Possible Region Transitions

In this paper a new relaxed stabilization criterion for discrete-time T-S fuzzy systems are proposed. First the operation state space is divided into several subregions and then the T-S fuzzy system is transformed to an equivalent switching fuzzy system. Consequently, based on the piecewise Lyapunov function, the stabilization criterion of the switching fuzzy system is derived. The main novelties of the criterion are as follows. (1) The positive definite matrix P_l corresponding to the subregion S_i instead of the traditional common P is found to satisfy the inequalities, (2) the successive two states of the system are considered in the inequalities. Due to the above two novelties, the criterion can be more relaxed. The proposed conditions in the criterion can be solved by means of linear matrix inequalities (LMIs) tools. An example is given to illustrate the advantage of the proposed criterion.