An LMI approach to robust H∞ control and stabilization analysis for uncertain T-S fuzzy systems with state and input time-delays

This paper presents the robust H_∞ control problems for a class of uncertain Takagi-Sugeno (T-S) fuzzy systems with time-delay where uncertainties involved in the state and input matrices. The T-S fuzzy model is employed to represent uncertain delayed nonlinear systems. A delay-dependent stabilization criterion is first presented and new conditions of stabilization for uncertain T-S fuzzy model with time-delay are given in the form of linear matrix inequalities (LMI) and based on Lyapunov-Krasovskii functional approach. The fuzzy feedback robust H_∞ controller is designed to stabilize the T-S fuzzy system to achieve the prescribed disturbance attenuation level. Numerical example is presented to demonstrate the effectiveness of the proposed method.