LMI-Based Approach for Output-Feedback Stabilization for Discrete-Time Takagi--Sugeno Systems

Static output-feedback stabilizing controllers for nonlinear systems represented by discrete-time Takagi--Sugeno fuzzy models are studied. The main result concerns the stabilization based on the parallel distributed compensation (PDC) approach. Sufficient conditions are provided for quadratic and nonquadratic stability. To design static output-feedback stabilizing controllers, a numerical procedure based on the cone complementarity algorithm is given. It is shown that the relaxed conditions proposed in the nonquadratic case outperform those for the quadratic case. Two numerical examples are given to illustrate the efficiency of the proposed approach.