摘要
Constructing a 'degenerate' Lyapunov functional and using Barbalat's lemma, we obtain a simple stability criterion for a system of neutral differential equations 6 1. IntroductionSufficient conditions for the uniformly asymoptic stability of the trivial solution of thelinear nonautonomous scalar delay differential equationand the vector matrix systemhave been obtained by Busenberg and cooke in [1]. It is found from the results of theseauthors that a decisive role is played by coefficients c(t) and C(t) of the nondelay terms in(1. 1) and (l. 2) in the process of constructing positive definite quadratic Lyapunov functionals whose derivatives are negative definite. If terms such as c(t) and C(t) in (1. 1 ) and(l. 2) are obsent, it is usually difficult to construct positive definite functionals; howeverit is a routine procedure to construct quadratic semidefinite functionals. In paper LZj, K.Gopalsamy has given sufficient conditions for asymptotic stability of the trivial solution ofthe coupled system of two autonomous neutral differential equationsIn this paper, we derive a set of sufficient conditions for the asymptotic stability of thetrivial solution of a system of nonautonomous neutral differential dquationswhere oil and al, are continuous real valued functions defined on [0, ￣), oil are differentiable and bounded, dij and rij are positive constants (i,j ￣ 1, 2, ..',n).
Constructing a 'degenerate' Lyapunov functional and using Barbalat's lemma, we obtain a simple stability criterion for a system of neutral differential equations 6 1. IntroductionSufficient conditions for the uniformly asymoptic stability of the trivial solution of thelinear nonautonomous scalar delay differential equationand the vector matrix systemhave been obtained by Busenberg and cooke in [1]. It is found from the results of theseauthors that a decisive role is played by coefficients c(t) and C(t) of the nondelay terms in(1. 1) and (l. 2) in the process of constructing positive definite quadratic Lyapunov functionals whose derivatives are negative definite. If terms such as c(t) and C(t) in (1. 1 ) and(l. 2) are obsent, it is usually difficult to construct positive definite functionals; howeverit is a routine procedure to construct quadratic semidefinite functionals. In paper LZj, K.Gopalsamy has given sufficient conditions for asymptotic stability of the trivial solution ofthe coupled system of two autonomous neutral differential equationsIn this paper, we derive a set of sufficient conditions for the asymptotic stability of thetrivial solution of a system of nonautonomous neutral differential dquationswhere oil and al, are continuous real valued functions defined on [0, ￣), oil are differentiable and bounded, dij and rij are positive constants (i,j ￣ 1, 2, ..',n).
