Quadratic Design of D-stabilizing Non-PDC Controllers for Quasi-LPV/T-S Models

This paper deals with the D-stabilization of quasi-LPV/Takagi-Sugeno (T-S) models. Based on a Quadratic Lyapunov Function (QLF) candidate, basic conditions are presented for the design of D-stabilizing Parallel Distributed Compensation (PDC) control, i.e with LMI region constraints. Then, relaxed quadratic LMI conditions are proposed in order to design a D-stabilizing non-PDC controller. The proposed results are illustrated in simulation through an academic example, then through the benchmark of the stabilization of a flexible robot with single joint.