Stability of retarded dynamical systems: A Lyapunov function approach

Four new stability theorems for general classes of retarded dynamical syste ms are established by using the Lyapunov function approach in this paper. A new technique is proposed for estimating the derivative of the Lyapunov fu nction along the solution of a system at some specific instant. It is remar ked that the stability conditions obtained by the established stability the orems together with the proposed technique are less conservative than those obtained by the existing Razumikhin-type theorems and techniques in the li terature. Four illustrative examples and two corollaries for systems with a single time-varying delay or multiple time-varying delays are given to sho w the applications of the established stability theorems and the proposed t echnique. (C) 2001 Academic Press.