Stability of functional differential equations of neutral type

Abstract

Abstract : A functional differential equation of neutral type is a differential system in which the rate of change of the system depends not only upon the past history but also the derivative of the past history of the system. For example, the system (1.1) x dot (t) + A x dot (t - 1) = f(t,x(t),x(t - 1)) is a functional differential or differential difference equation of neutral type. It is the purpose of this paper to give sufficient conditions for the stability and instability of solutions of a large class of equations (1.1) in terms of functions similar to those occurring in the application of the second method of Liapunov to ordinary and functional differential equations of retarded type. The basic restriction on the class of systems is that the derivatives occur linearly with coefficients depending only upon t and that the 'difference' operator associated with the equation is stable. (Author)