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Stability radius and internal versus external stability in Banach spaces: An evolution semigroup approach. (English) Zbl 0978.47030
The authors study stability of infinite-dimensional linear control systems by means of the theory of evolution semigroups. This approach allows one to apply the classical theory of strongly continuous semigroups to the time-varying systems. In particular, the complex stability radius is expressed in terms of the generator of the evolution semigroup. the authors also study the explicit relationship between internal and external stability.

MSC:
47D06One-parameter semigroups and linear evolution equations
34G10Linear ODE in abstract spaces
93C25Control systems in abstract spaces
93D09Robust stability of control systems
93D25Input-output approaches to stability of control systems