INTEGRAL REPRESENTATION FORMULA FOR LINEAR NONAUTONOMOUS DIFFERENCE-DELAY EQUATIONS

Abstract

We state and prove an integral representation formula of the “variation-of-constant” type for continuous solutions of linear nonautonomous difference-delay systems, in terms of a Lebesgue–Stieltjes integral involving a fundamental solution and the initial data of the system. This gives a precise and correct version of several formulations appearing in the literature, and extends them to the time-varying case. This is of importance for further stability studies of various kinds of delay systems.