Relaxed static output stabilization of polynomial fuzzy control systems by Lagrange membership functions

This article is concerned with the stability analysis of the static output-feedback polynomial fuzzy-model-based (SOF PFMB) control systems through designing a novel membership grade integration (MGI) approach. The nonconvex problems of the SOF PFMB control systems are convexificated into the convex conditions by introducing block diagonal positive-definite Lyapunov matrix and nonsingular transformation matrix. We proposed new approximate membership functions, that is, Lagrange membership functions (LMFs), which can be introduced into the stabilization process to relieve the conservativeness of stability results. The LMFs are general representations of piecewise-linear membership functions, which makes the number of stability conditions not limited by the number of sample points. In a fixed subdomain, arbitrary sample points can be employed by the LMFs method and achieve higher approximation capability by increasing more sample points so that membership grades can be incorporated into the system analysis. Furthermore, a novel MGI approach, including the information of premise variables and LMFs, is proposed making the stability conditions more relaxed. Finally, two simulation examples show the merits of the developed techniques.