An Evolution Equation Approach to Nonautonomous Linear Systems with State, Input, and Output Delays

We propose a new approach which brings nonautonomous linear systems with state, input, and output delays in the line with the standard theory of nonautonomous linear systems. To this purpose, we establish, using the concept of Lebesgue extensions, a new variation of constants formula for nonhomogenous delay equations. From this we deduce another new one for nonautonomous linear systems with state and input delays. Inspiriting from this formula we show that a given delay system determines a nonautonomous absolutely regular linear system with the same input and output spaces as of the delay system. Our abstract results will be applied to investigate the existence and the uniqueness of the solutions for a class of nonautonomous neutral equations in Banach spaces.