Resilient guaranteed cost control to tolerate perturbations for uncertain singular systems

The resilient guaranteed cost control (RGCC) problem is studied in this paper for a class of uncertain singular systems with a given quadratic cost function. The uncertainty in the system is assumed to be norm-bounded and time-varying. The problem is to design a state feedback control law such that the closed-loop systems are regular, stable, and impulse-free, while the cost index of the closed-loop systems is within a certain bound for all these admissible uncertainties. Sufficient conditions for the existence of resilient guaranteed cost controller are given by Riccati equalities. The design of the resilient guaranteed cost controller and the corresponding guaranteed cost of the systems are obtained. Finally, a numerical example is given to illustrate the design method.