ASYMPTOTIC STABILITY OF RETARDED FUNCTIONAL DIFFERENTIAL EQUATIONS BY LYAPUNOV’ DIRECT METHOD

This paper is devoted to studying the asymptotic stability of retarded nonlinear functional differential equations by the method of Lyapunov functionals. Under the as-sumption that there exists a positive definite time-invariant Lyapunov functional with negative semi-definite derivative, we focus on the extra conditions to guarantee the asymptotic stability, and present a new criterion, which is less conservative than the classical one. Finally, an example is given to illustrate the effectiveness of the result.