Robust stabilization of the Takagi-Sugeno fuzzy model via bilinear matrix inequalities

Quadratic stability has enabled, mainly via the linear matrix inequality framework, the analysis and design of a nonlinear control system from the local matrices of the system´s Takagi-Sugeno (T-S) fuzzy model. It is well known, however, that there exist stable differential inclusions, hence T-S fuzzy models whose stability is unprovable by a globally quadratic Lyapunov function. At present, literature in the broader area of stability analysis suggests piecewise-quadratic stability as a means to avoid such conservatism. This paper generalizes the idea and proposes a framework that supports less conservative sufficient conditions for the stability of the T-S model by using piecewise-quadratic generalized Lyapunov functions. The advocated approach results in the formulation of the controller synthesis, which, herein, aims for robust stabilization, as a problem of bilinear rather than linear matrix inequalities. Simulation studies, which include an algorithm for solution of bilinear matrix inequalities, demonstrate the proposed method