Quadratic Optimal Control with Disturbance Attenuation for Uncertain Continuous-Time T-S Fuzzy Systems

In this study, an algebraically computational method is proposed to synthesize non-parallel-distributed-compensation (non-PDC) fuzzy controller such that (1) the prescribed disturbance attenuation level for the uncertain continuous-time Takagi-Sugeno (T-S) fuzzy system can be achieved, and (2) a quadratic integral performance index for nominal T-S fuzzy model-based control system can be minimized. We first derive relaxed linear matrix inequality (LMI) conditions by non-quadratic Lyapunov function and non-PDC fuzzy controller to meet prescribed disturbance attenuation level for the uncertain T-S systems. Then by using LMIs and orthogonal function array, the robust quadratic optimal control with disturbance attenuation for uncertain T-S fuzzy system is transformed into constrained-optimization problem represented by algebraic equations and LMI constraints. For static constrained-optimization problem, the HTGA is employed to search the gains non-PDC controllers. Therefore, the robust optimal controller design problem can be greatly simplified with the proposed method. The design example is given to demonstrate the applicability of the proposed approach.