Delay-dependent adaptive control of uncertain time-delay systems

In this article, delay-dependent adaptive control algorithms are developed for closed-loop stabilization of a class of uncertain time-delay systems with time-varying delay and nonlinear dynamical perturbation. The norm of the nonlinear perturbation is assumed to be bounded by a weighted norm of the state. Two main problems are investigated. In the first problem, an adaptive control scheme is developed to guarantee asymptotic stabilization of the closed-loop system when the weight of the state norm is assumed to be known. In the second problem, asymptotically stabilizing adaptive controller is derived when the weight of the state norm is assumed to be unknown. A numerical simulation example, that illustrates the two design approaches, is presented.