Quadratic Design of Robust Controllers for Uncertain T-S Models with D-Stability Contraints

This paper deals with the robust D-stabilization of uncertain Takagi-Sugeno (T-S) fuzzy systems. New Linear Matrix Linearity (LMI) conditions are proposed for the design of non Parallel-Distributed-Compensation (non-PDC) controllers with D-stability constraints, i.e forcing the poles of each linear polytopes of the closed-loop T-S plant with model uncertainties to belong in a prescribed LMI region. The LMI conditions are obtained through the use of a quadratic Lyapunov function candidate and relaxed by the introduction of free weighting matrices. To illustrate the effectiveness of the proposed approach, the D-stabilization of an academic example of a fourth-order uncertain T-S model is provided in simulation.