GLOBAL EXPONENTIAL STABILIZATION OF NONLINEAR NON-AUTONOMOUS DIFFERENTIAL EQUATIONS VIA RICCATI EQUATIONS

Abstract

This paper considers the exponential stabilization of a class of nonlinear functional differential equations. The system to be considered is non-autonomous and the delay is time-varying. Using an improved Lyapunov-Krasovskii functional, we establish new suffcient conditions for the global exponential stabilizability in terms of the solution of Riccati differential equation without controllability assumption and restriction on the nonlinear perturbation. These conditions allow to compute simultaneously the two bounds that characterize the stability rate of the solution.