Memoryless adaptive robust state feedback controllers of uncertain dynamical systems with time-varying delays

The problem of adaptive robust stabilization is considered for a class of dynamical systems with multiple time-varying delayed state perturbations, time-varying uncertain parameters, and external disturbances. It is assumed that the upper bounds of the delayed state perturbations, uncertainties, and external disturbances are unknown, and that the time-varying delays are any nonnegative continuous and bounded functions, and do not require that their derivatives have to be less than one. For such a class of uncertain time-delay systems, a new method is presented whereby a class of continuous memoryless adaptive robust state feedback controllers is proposed. By employing a quasi-Lyapunov function, it is shown that the uniform ultimate boundedness of uncertain time-delay systems can be guaranteed. In addition, since the proposed adaptive robust state feedback controllers are completely independent of time delays, the results obtained in the paper may be also applicable to a class of dynamical systems with uncertain time delays. Finally, a numerical example is given to demonstrate the validity of the results.