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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 wellposed 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 stabilizability of delay systems is presented, which extends the wellknown results for finite dimensional(More)
The feedback stabilizability is an interesting and difficult subject in systems theory. In the finite-dimensional context, the problem of stabilizability is well-established using the so-called Hautus criterion, see e.g. [3]. In the infinite-dimensional context, this problem is quite difficult and only partial answers are obtained under extra assumptions on(More)
A semigroup approach for the well-posedness of perturbed nonhomogeneous abstract boundary value problems is developed in this paper. This allows us to introduce a useful variation of constant formula for the solutions. Drawing from this formula, necessary and sufficient conditions for the approximate controllability of such systems are obtained, using the(More)