An LMI approach to reliable guaranteed cost control of discrete-time systems with actuator failure

This paper is concerned with the reliable guaranteed cost control problem for discrete-time systems with actuator failures and a given quadratic cost function. The problem is to design a reliable guaranteed cost state feedback control law which can tolerate actuator failure, such that the cost function of the closed-loop system is guaranteed to be no more than a certain upper bound. A sufficient condition for the existence of reliable guaranteed cost controllers is derived via the linear matrix inequality (LMI) approach, and a design procedure of such controllers is presented. Furthermore, a convex optimization problem with LMI constraints is formulated to design the optimal reliable guaranteed cost controller which minimizes the upper bound of the closed-loop system cost.