Robust guaranteeing-cost stability for discrete time-delay systems with nonlinear perturbation

The problems of robust stability and robust stability with a guaranteeing-cost for time-delay systems with nonlinear perturbation are discussed. A sufficient criterion for robust stability is established in a LMI framework and a linear convex optimization problem with LMI constraints for computing maximal perturbation bound is proposed. Meanwhile, a sufficient criterion for robust stability with a guaranteeing-cost for such systems is obtained, and an optimal procedure for decreasing the value of guaranteeing cost is put forward. An example illustrates the efficiency of our results.