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 tim...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.展开更多
基金supported by the National Basic Research Program of China (973 Program,Grant No.2005CB321902)the National Natural Science Foundation of China (Grant No.60473109+1 种基金No.60374001)the Doctor Fund of Ministry of Education of China (No.20030006003)
文摘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.
