H∞ robust controller for discrete-time linear systems under control and output constraints

This work deals with H_∞ robust control problem for discrete-time systems subject to parameter uncertainty and control and output constraints. The uncertainties are polytopic and the dynamic output feedback controller is considered. The designed controller is expressed as a feasibility problem of a bilinear matrix inequality (BMI), that is based on the existence of an ellipsoidal positively (D, R)-invariant set, generated by quadratic Lyapnuov function, contained in the systems domain of linearity. Using Differential Evolution (DE) and LMIs, a hybrid algorithm is proposed for searching an optimal robust controller.