Robust optimal control for a class of nonlinear uncertain singular systems with time-delay

The guaranteed cost control problem for a class of nonlinear singular systems with time-delay is studied in this paper. The problem is to design a memoryless state feedback controller such that the closed-loop system is asymptotically stable and the closed-loop cost function value is less than a specified upper bound for all admissible uncertainties. A sufficient condition for the existence of such controllers is presented in terms of the solvability to a certain system of LMIs, and a parametrized representation of a set of guaranteed cost controllers is provided by the feasible solutions to the system of LMIs. Furthermore, a procedure is given to select an optimal guaranteed cost control law in the sense of minimizing the upper bound of the cost function