An LMI method to reliable guaranteed cost control of continuous-time systems with actuator failure

This paper investigates the design of the reliable guaranteed cost control problem for continuous-time systems with actuator failures. The actuator failure model is formulated. Based on this model, 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) method, and by using Matlab, this controller is easy to implement. 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. Finally, a numerical example is given to illustrate the effectiveness of the proposed design method.