Abstract
In this paper, by using the concept of Yosida distance between two closed linear operators, we study the stability radius r(A) of linear systems u′(t)=Au(t), where A is the generator of an analytic semigroup, under unbounded perturbations in this class of generators. We show that r(A)=1/sups∈R‖R(is,A)‖L(X), so extending a classic result by Henrichsen and Pritchard to the infinite-dimensional case. A formula of the dichotomy radius is also established. Finally we give an estimate of the stability radius of general C0-semigroups. Two examples from a parabolic equation are given.
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