Stability radius and internal versus external stability in Banach spaces: an evolution semigroup approach

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dc.creatorClark, Stephen
dc.creatorLatushkin, Yuri
dc.creatorMontgomery-Smith, Stephen J.
dc.creatorRandolph, Tim
dc.date1998-11-27
dc.date1999-12-08
dc.date.accessioned2026-07-07T05:27:00Z
dc.date.available2026-07-07T05:27:00Z
dc.descriptionIn this paper the theory of evolution semigroups is developed and used to provide a framework to study the stability of general linear control systems. These include time-varying systems modeled with unbounded state-space operators acting on Banach spaces. This approach allows one to apply the classical theory of strongly continuous semigroups to time-varying systems. In particular, the complex stability radius may be expressed explicitly in terms of the generator of a (evolution) semigroup. 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 provided for these general 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
dc.descriptionAlso at http://www.math.missouri.edu/~stephen/preprints
dc.identifierhttps://arxiv.org/abs/math/9811160
dc.identifierhttp://arxiv.org/abs/math/9811160
dc.identifierS.I.A.M. J. of Control Optim, 38, (2000), 1757-1793.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/77766
dc.subjectDynamical Systems
dc.subjectAnalysis of PDEs
dc.subjectFunctional Analysis
dc.subjectOperator Algebras
dc.subjectOptimization and Control
dc.subject47D06, 34G10, 93C25, 93D09, 93D25
dc.titleStability radius and internal versus external stability in Banach spaces: an evolution semigroup approach
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