Optimal guaranteed cost control of singular systems with delayed state and parameter uncertainties

The guaranteed cost control problem via memoryless state feedback controllers is studied in this paper for a class of linear singular systems with delayed state and norm-bounded time-varying parameter uncertainties. A sufficient condition for the existence of guaranteed cost controllers is derived, and it is shown that the condition is equivalent to the solvability of a certain linear matrix inequality (LMI). Furthermore, 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 system.