Adaptive robust control of uncertain dynamical systems with multiple time-varying delays

The problem of adaptive robust stabilisation 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 non-negative continuous and bounded functions. In particular, it is not required that the derivatives of time-varying delays have to be less than one. For such a class of uncertain time-delay systems, a new method is presented whereby a class of memoryless continuous adaptive robust state feedback controllers is proposed. By employing a quasi-Lyapunov function, it is shown that the solutions of uncertain time-delay systems can be guaranteed to be uniformly exponentially convergent towards a ball which can be as small as desired. In addition, since the proposed adaptive robust state feedback controllers are completely independent of time delays, the results obtained in the study 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.