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

Abstract

The guaranteed cost control problem via memory less 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.