We show that the class of regular time varying systems is invariant under perturbations by time–varying state and input delays. In particular, we give explicit formulas of the resulting input, output, and input–output maps. This result is used to solve the feedback problem for the delayed system. The relationship between the open and the closed loop system… (More)
—The feedback stabilizability of a general class of well-posed linear systems with state and input delays in Banach spaces is studied in this paper. Using the properties of infinite dimensional linear systems, a necessary condition for the feedback sta-bilizability of delay systems is presented, which extends the well-known results for finite dimensional… (More)
— In this paper, admissibility of control operators for perturbed semigroups is considered. We prove that the set of admissible control operators for a semigroup generator is unchanged if we perturb this generator by an appropriate class of unbounded operators. The result is applied to prove the well-posedness of a class of time-delay systems.