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.
- input delay
- state delay
- norm-bounded uncertainties
Parlakçι, M. N. A., & Küçükdemiral, I. B. (2010). Robust delay-dependent stabilizing control of time-delay systems with state and input delays: augmented L.K. functional approach. In T. Vyhlidal, & P. Zitek (Eds.), 9th IFAC Workshop on Time Delay Systems (2 ed., Vol. 43, pp. 212-217). Elsevier B.V.. https://doi.org/10.3182/20100607-3-CZ-4010.00039