Optimal guaranteed cost control for uncertain time-varying delay systems

This paper studies the problem of guaranteed cost control for a class of time-varying uncertain continuous time-delay systems with both state and input delays. Suppose that the time-varying uncertain parameters are norm-bounded, but the matched conditions are not required to satisfy. A new sufficient condition of satisfying guaranteed cost index is given for the systems by constructing Lyapunov function and linear matrix inequalities approach. Guaranteed cost controllers can be obtained only from solving corresponding linear matrix inequalities such that a guaranteed cost function for the closed-loop systems has an upper bound irrespective of all admissible parameters uncertainties. Optimal guaranteed cost controllers can be obtained from solving corresponding convex optimization. Furthermore, a numerical example is given to show the potential of the proposed techniques.