Reliable Guaranteed Cost Control of Nonlinear Uncertain Discrete-Time Systems with Time-Varying State Delay and Actuator Failure

This paper concerns the reliable guaranteed cost control problem of nonlinear uncertain discrete-time systems with time-varying state delay and actuator failures for a given quadratic cost function. The problem is to design a reliable guaranteed cost state feedback control law which can tolerate actuator failures, such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound. Based on the linear matrix inequality (LMI) approach, a sufficient condition for the existence of reliable guaranteed cost controllers is derived. 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. A numerical example is given to illustrate the proposed method.