Robust $\mathcal{L}_{2}$ Control for Uncertain T-S Descriptor Model with Input Saturation

Abstract : This paper concerned with the stabilization of uncertain discrete-time descriptor models subject to input saturation and external disturbances. The design control strategy is based on Takagi-Sugeno (T-S) approach and a non parallel distributed compensation control law. To synthesis the fuzzy controller, the stability conditions are derived using non-quadratic Lyapunov functions with respect to the given saturation constraint on the control input and achieving a guaranteed L2-gain performance. The optimization problem is formulated in terms of linear matrix inequalities (LMIs). Numerical example illustrates the efficiency of the proposed approaches.