97-144 Latushkin, Y., Montgomery-Smith S., Randolph, T.
Evolution semigroups and robust stability of evolution operators on Banach spaces (74K, LaTeX2e) Mar 24, 97
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Abstract. Using the theory of evolution semigroups, this paper investigates the stability radius for a wide class of linear nonautonomous systems in Banach spaces. A spectral-mapping theorem for evolution semigroups acting on vector-valued functions on $[0,\infty)$ is proven first. This allows the stability radius to be expressed in terms of the spectrum of the generator of the evolution semigroup. Consequences include explicit formulas for bounds on the stability radius for Banach space systems; time-varying and constant perturbations are considered.

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