We investigate the infinite dimensional control linear systems with delays in the state and input. We give a new variation of constants formula when the state and control delay operators are unbounded. We prove the existence of mild and classical solutions of such systems. Our approach is based on the theory of abstract and regular linear systems introduced by Salamon (Math Syst Theor 21: [147][148][149][150][151][152][153][154][155][156][157][158][159][160][161][162][163][164] 1989) and Weiss (Isr J Math 65:17-43, 1989). Finally, we apply our abstract framework to an example from population dynamics.

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In this work, we prove that the exact controllability of linear autonomous systems are conserved with "small" Desch-Schappacher perturbations arising, e.g., from the perturbations of dynamic operator's domain. Our results are illustrated by an application to controlled systems with dynamic and boundary perturbations.  2004 Elsevier Inc. All rights reserved.