Improved stability and stabilization conditions for Takagi-Sugeno fuzzy systems via fuzzy lyapunov functions

This paper deals with the stability analysis and control design problems for continuous-time Takagi-Sugeno (TS) fuzzy systems. By employing a novel fuzzy Lyapunov function and the parallel distributed compensation control scheme, sufficient stability conditions of fuzzy systems are derived. Unlike conventional approach based on quadratic Lyapunov functions, the bound of the time-derivatives of membership functions is not required in the proposed approaches. Based on the result of Geromel and Korogui [31] combined with the property of dual system, new sufficient conditions for the existence of fuzzy controller under consideration are achieved in terms of linear matrix inequalities (LMIs). Moreover, the expressions of desired fuzzy controller are given.