Global Asymptotic Stabilization of Uncertain Time-delay Systems

Abstract

To this end, the unit feedback synthesis is developed for a class of uncertain timedelay systems with nonlinear disturbances and unknown delay values whose unperturbed dynamics are linear. Being inspired from [179], the present synthesis is based on the delay-dependent stability criterion, which is derived within the framework developed in Sect. 3.8. The controller constructed proves to be robust against sufficiently small delay variations and weak external (possibly, unmatched) disturbances. It is worth noticing that allowing unmatched disturbances is a step beyond a standard sliding mode control treatment. Specifically, the critical delay value when the closed-loop system, corresponding to this value, becomes asymptotically unstable, is explicitly calculated as a function of linear growth constants of the unmatched disturbances. Performance issues of the controller are illustrated in a simulation study.