Nonfragile guaranteed cost control for uncertain nonlinear discrete-time systems with time-varying state delay

This paper concerns the nonfragile guaranteed cost control problem for a class of nonlinear discrete-time dynamic systems with time-varying delay and controller gain perturbations. Guaranteed cost control law is designed under two classes of perturbations, namely, additive form and multiplicative form. The problem is to design a memoryless state feedback control law such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties. Some delay-dependent conditions for the existence of such controller are derived. A numerical example is given to illustrate the proposed method.