Relaxed stabilization criteria for discrete-time T-S fuzzy control systems based on a switching fuzzy model and piecewise Lyapunov function

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 S_j are presented by one matrix X_j. 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.