Robust H∞ control for a class of uncertain T-S fuzzy system with time delay

The problem of delay-dependent H_infin control for a class of uncertain T-S fuzzy systems with time delay is studied based on free weighting matrices. First, free weighting matrices are introduced in the derivative of the Lyapunov-Krasovskii functional. Based on Lyapunov stability method, a new delay-dependent robust stability criterion is proposed. The new criterion is less conservative than the exiting ones. Based on the stability criteria, sufficient condition for the existence of fuzzy H_infin state feedback controller is devised in the form of non-linear matrix inequality. Parameter setting method and Schur complement are employed to transform nonlinear matrix inequality into linear matrix inequality. Finally, a simulation example is given to illustrate the effectiveness of the proposed method.