Robust stabilization of uncertain dynamic time-delay systems with unknown bounds of uncertainties

The problem of robust stabilization for a class of uncertain dynamic systems with state and multiple delayed state perturbations is considered. It is assumed that each perturbation of state and time-delayed state is bounded by a linear function with unknown gains. For such uncertain systems, two classes of continuous state feedback controllers are proposed in this paper. Based on Lyapunov stability theory and Lyapunov-Krasovskii function, a robust adaptive feedback controller is proposed. By employing Razumikhin lemma, we also develop a novel nonlinear feedback controller. Both the controllers are completely independent of the time delays and can render the closed-loop systems globally stable in the sense of uniform ultimate boundedness. Finally, a numerical example is given to demonstrate the validity of the results.