Guaranteed Cost Control of Quadratic Time-Delay Systems

This paper deals with the problem of regional guaranteed cost control design for, possibly open-loop unstable, nonlinear quadratic systems with a delayed state. Control methods based on the Razumikhin and Lyapunov-Krasovskii stability theorems are developed for designing static nonlinear quadratic state feedback controllers that achieve delay-independent regional stability while guaranteeing a quadratic regulator-type performance for any initial function taking value in a region of the state-space inside some polytopic domain. The proposed methods are tailored via a finite set of linear matrix inequalities. A numerical example is presented to illustrate the potentials of the control designs.