Delay-Dependent Regional Stabilization of Nonlinear Quadratic Time-Delay Systems

This paper addresses the synthesis of delay-dependent local stabilizing controllers for, possibly open-loop unstable, nonlinear quadratic systems with a varying time-delay in the state. We develop methods for designing static nonlinear quadratic state feedback controllers that guarantee the local asymptotic stability of the closed-loop system zero equilibrium point in some polytopic region of the state-space while ensuring a region of stability inside this polytope. Control designs based on either the Razumikhin or the Lyapunov-Krasovskii approaches are considered. The proposed designs are delay-dependent and are formulated in terms of linear matrix inequalities. A numerical example is presented to illustrate the application of the stabilization methods.