Reliable robust guaranteed cost and D-stability control for delta operator linear uncertain systems

The reliable robust guaranteed cost and D-stability control problem is investigated for a class of delta operator formulated linear uncertain systems subject to actuator failure. The purpose is to design a state feedback controller which can tolerate actuator failures, such that the cost function of the closed-loop system is guaranteed to be no more than a certain upper bound, and the poles of the closed-loop system are located in an expected disk on complex plane. A sufficient condition for the existence of such controllers is obtained via the linear matrix inequality approach. Furthermore, a convex optimization problem is presented to design the optimal reliable robust guaranteed cost controller which minimizes the upper bound of the closed-loop cost.