Adaptive stabilizing state feedback controllers of uncertain dynamical systems with multiple time delays

The problem of robust stabilization for a class of uncertain dynamical systems with multiple delayed state perturbations is considered. In this paper, it is assumed that each perturbation is bounded by a linear function of delayed state with unknown gains, and an adaptation law is proposed to estimate these unknown gains. Moreover, by making use of the updated values of these unknown bounds we propose a memoryless state feedback controller for such a class of uncertain time-delay systems. Based on Lyapunov stability theory and Lyapunov-Krasovskii functional, it is shown that the closed-loop dynamical system resulting from the proposed adaptive robust control schemes is globally stable in the sense of uniform ultimate boundedness. Finally, a numerical example is given to demonstrate the validity of the results