Mathematics – Dynamical Systems
Scientific paper
1998-11-27
S.I.A.M. J. of Control Optim, 38, (2000), 1757-1793.
Mathematics
Dynamical Systems
Also at http://www.math.missouri.edu/~stephen/preprints
Scientific paper
In 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
Clark Stephen
Latushkin Yuri
Montgomery-Smith Stephen J.
Randolph Tim
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