Global asymptotic stability of nonlinear delayed systems of neutral type

Abstract

Global asymptotic stability of delayed differential equation of neutral type with off-diagonally increasing right-hand side is considered. First, it is shown that by using a special form of variable transformation, the considered system can be reduced to a differential difference inequality of retarded type. The stability of the trivial solution of the given system is studied with the help of thus obtained inequality. This is a development of the approach previously presented by Ma et al. However, the condition so far obtained on the nonlinear cases by Ma et al. (Nonlinear Anal. Theory Methods Appl. 33 (4) (1998) 367) is rather restrictive and these restrictions are somewhat similar to those for linear systems. In short, the nonlinear cone of invariant region, with the origin as its head, constructed by nonlinear functions, must contain a linear cone inside it. The object of this report is to remove such restriction.