ADAPTIVE ROBUST CONTROL FOR A CLASS OF UNCERTAIN TIME–DELAY SYSTEMS VIA OUTPUT FEEDBACK

The problem of robust stabilization is considered for a class of systems with the delayed state perturbations, uncertainties, and external disturbances. It is assumed that the upper bounds of the delayed state perturbations, uncertainties, and external disturbances, are unknown. An improved adaptation law with s–modification is first introduced to estimate these unknown bounds. Then, by making use of the updated values of the unknown bounds, a class of adaptive robust output feedback controllers is proposed. On the basis of the strictly positive realness of the nominal system, it is also shown from the Kalman–Yakubovitch lemma that the solutions of the resulting adaptive closed–loop time-delay system can be guaranteed to be uniformly bounded, and the states decreases uniformly asymptotically to zero. Finally, a numerical example is given to demonstrate the validity of the results.