Robust state feedback controllers of uncertain time-delay systems with completely unknown bounds of uncertainties

Abstract

In this paper, the problem of robust stabilization is considered for a class of uncertain time-delay dynamical systems with completely unknown upper bounds of the delayed state perturbations, uncertainties, and external disturbances. For such a class of uncertain time-delay dynamical systems, a new design method is presented whereby a class of continuous memoryless adaptation-free robust state feedback controllers is constructed. That is, no adaptation law is introduced to update those completely unknown upper bounds. It is also shown that the solutions of the resulting closed-loop time-delay dynamical systems can be guaranteed to be uniformly exponentially bounded, instead of uniform ultimate boundedness. Finally, as an application of the results, the problem of water pollution control is considered for uncertain river time-delay systems due to industrial waste treatment facility, and the corresponding simulations are provided to demonstrate the validity of the theoretical results.