Stability Analysis and Stabilization of Fuzzy State Space Models

Fuzzy control has achieved numerous successful industrial applications. However, stability analysis for fuzzy control systems remains a difficult problem, and most of the critical comments on fuzzy control are due to the lack of a general method for its stability analysis. Although significant research efforts have been made in the literature, appropriate tools for this issue have yet to be found. This thesis focuses on the problem of stability of fuzzy control systems. Both linguistic fuzzy models and T-S fuzzy models are discussed. The main work of this thesis can be summarized as follows: (1). A necessary and sufficient condition for the global stability of linguistic fuzzy models is given by means of congruence of fuzzy relational matrices. (2). A hyperellipsoid-based approach is proposed for stability analysis and control synthesis of a class of T-S (affine) fuzzy models with support-bounded fuzzy sets in the rule base. (3). Approaches of BMI-based fuzzy controller designs are proposed for the stabilization of T-S fuzzy models. (4). For the general T-S type fuzzy systems with norm-bounded uncertainties and time-varying delays, sufficient robust stabilization conditions are presented by employing the PDC-based fuzzy state feedback controllers. On stability analysis of T-S fuzzy models, most reported results based on the method of common quadratic Lyapunov functions require that each subsystem of the fuzzy models be stable in order to guarantee the stability of the overall systems. This restriction is overcome in our results by means of employing the structural information in the fuzzy rules.