Guaranteed cost control of linear uncertain systems with time-varying delays in state and input: An LMI approach

The guaranteed cost control problem via memoryless state feedback controllers is studied in this paper for a class of linear time-varying delay systems with norm-bounded time-varying parametric uncertainty and a given quadratic cost function. The time-varying delays are assumed bounded but no information to be available. Sufficient conditions for the existence of guaranteed cost controllers are given in terms of linear matrix inequalities (LMI's). A convex optimization problem with LMI constraints is formulated to design the optimal guaranteed cost controller, which minimizes the guaranteed cost of the closed-loop uncertain systems with multiple time-varying delays in state and input. The results obtained in this paper can be easily extended to the multiple time-delays case.