Optimal Robust Guaranteed Cost Control of Uncertain Linear Continuous Time Systems via Dynamical Output Feedback

The optimal robust guaranteed cost control problem via dynamical output feedback is studied in this paper for a class of linear continuous time systems with norm-bounded time-varying parametric uncertainties and a given quadratic cost function. Sufficient conditions for the existence of guaranteed cost controllers and a control design method are given in terms of linear matrix inequalities (LMIs). Such that the closed-loop system with cost functions has an upper bound irrespective of all admissible uncertainties. Furthermore, a convex optimization problem with LMI constraints is formulated to design the optimal robust guaranteed cost controller which minimizes the guaranteed cost of the closed-loop uncertain system. An algorithm of the proposed approach is given