Adaptive robust state feedback controllers for a class of dynamical systems with delayed state perturbations

The problem of robust stabilization for a class of dynamical systems with delayed state perturbations is considered. In this paper, the bound of the delayed state perturbations is assumed to be unknown, and an adaptation law is proposed to estimate this unknown bound. Moreover, by making use of the updated values of this unknown bound we propose a memoryless state feedback controller. Based on the Lyapunov-Krasovskii functional, it is shown that the closed-loop 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