# On structured perturbations for two classes of linear infinite-dimensional systems

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## Abstract

This paper considers two classes of infinite-dimensional systems described by an abstract differential equation*x* (*t*) = (*A + BΔC*)*x*(*t*),*x*(0) =*x*_{0}, on a Hilbert space, where*A, B, C* are linear, possibly unbounded operators and Δ is an unknown, linear, bounded perturbation. The two classes of systems are defined in terms of properties imposed on the triple (*A, B, C*). It is proved that for every Δ the perturbed system (*A + EΔF, B, C*) inherits all the properties of the unperturbed system {*A, B, C*}) if (*A, E, F*) and {*A, B, F*} are in the same class.

## Keywords

Hilbert Space Unbounded Operator Unperturbed System Bounded Perturbation Structure Perturbation
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© Kluwer Academic Publishers 1996