Robust Delay-Dependent Stabilizing Control of Time-Delay Systems with State and Input Delays: Augmented L.K. Functional Approach

In this paper, we investigate the design problem of a stabilizing control for a class of linear uncertain time-delay systems with time-varying state and input delays. The control law is selected to be a state-feedback controller. Adopting to employ an augmented type of Lyapunov-Krasovskii functional, for the nominal case, we first derive some sufficient delay-dependent stabilization criteria which can be solved using a convex optimization technique with interior-point algorithms. The stabilization synthesis is then extended to the case when the time-delay system is subject to the norm-bounded uncertainties which affect state and input matrices. Several numerical examples are presented to demonstrate the application of the proposed synthesis of a stabilizing controller. The numerical results on the maximum allowable delay bound and the uncertainty bound seem to be quite less conservative in comparison to the existing methods from the literature.