A new fuzzy lyapunov function approach to stability analysis and control synthesis for Takagi-Sugeno fuzzy systems

This paper addresses the problem of the stability analysis and control synthesis for continuous-time TakagiSugeno (TS) fuzzy systems. By employing the descriptor system approach and the parallel distributed compensation control scheme, sufficient stability conditions of fuzzy systems are derived based on a novel fuzzy Lyapunov function. Unlike conventional approach using a fuzzy blending of multiple quadratic Lyapunov functions, the bound of the time-derivatives of membership functions is not required in the proposed methods. In addition, the proposed methods overcome the difficulty using the fuzzy Lyapunov functions usually lead to solver the bilinear matrix inequalities. New sufficient conditions for TS fuzzy models allow a straightforward formulation in terms of linear matrix inequalities (LMIs), which can be easily solved by convex optimization techniques. Finally, a numerical example is given to the effectiveness of proposed methods.