Relaxed Static Output Feedback Control for T-S Fuzzy Systems Based on a Switching Sequence Convex Optimization Algorithm

This article is concerned with the static output feedback stabilization problem of T-S fuzzy systems by developing a novel switching sequence convex optimization (SSCO) algorithm. First, the time-varying relaxation matrix with time-varying properties is introduced, which combines the membership functions and the constructed switching mechanism to adjust the positive and negative terms of the inequality conditions, thereby improving the relaxation quality of stability conditions. To compute bilinear matrix inequalities (BMIs) with complex time-varying relaxation matrix structures, the developed SSCO algorithm employs a more flexible switching-type optimization variable and an inner approximation strategy capable of linearizing all concave sections. As a result, a sequence of linear matrix inequalities (LMIs) are obtained without introducing any additional constraint and with better approximation level than existing solving methods. The superiority of the proposed method includes two aspects: more relaxed solving conditions are gained by using the time-varying relaxation matrix technique to facilitate controller design; the proposed SSCO algorithm is of faster convergence rate, which means less computational time for practical implementation. Finally, the proposed relaxed switching control method is validated by simulation comparison.