Stabilization of Quadratic Time-Delay Systems with a Guaranteed Region of Stability1

This paper addresses the problem of local stabilization of open-loop unstable nonlinear quadratic state-delayed systems with a guaranteed region of stability. For some polytopic region of the state-space containing the origin, we develop linear matrix inequality based methods for designing nonlinear static state feedback controllers by considering either the Lyapunov-Razumikhin approach or a Lyapunov-Krasovskii functional. A numerical example illustrates the potentials of the proposed local stabilization methods.