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Examples are given to show that classical formulas for the stability radius of an autonomous Hilbert-space system fail in more general settings. Upper and lower bounds on the stability radius are proven for Banach-space systems. In addition, it is shown that the theory of evolution semigroups allows for a straightforward operator-theoretic analysis of internal stability as determined by classical frequency-domain and input-output operators, even for nonautonomous Banach-space systems. In particular, for the nonautonomous setting, internal stability is shown to be equivalent to input-output stability for stabilizable and detectable systems. For the autonomous setting, an explicit formula for the norm of input-output operator is given.<\/jats:p>","DOI":"10.1137\/s036301299834212x","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"1757-1793","source":"Crossref","is-referenced-by-count":34,"title":["Stability Radius and Internal Versus External Stability in Banach Spaces: An Evolution Semigroup Approach"],"prefix":"10.1137","volume":"38","author":[{"given":"Stephen","family":"Clark","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuri","family":"Latushkin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Stephen","family":"Montgomery-Smith","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Timothy","family":"Randolph","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,26]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1002\/mana.3211860102"},{"key":"R2","doi-asserted-by":"crossref","unstructured":"W. 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