Stability radius and internal versus external stability in Banach spaces: An evolution semigroup approach. (English) Zbl 0978.47030

Clark, Stephen; Latushkin, Yuri; Montgomery-Smith, Stephen; Randolph, Timothy

SIAM J. Control Optimization 38, No. 6, 1757-1793 (2000).

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.

Reviewer: V.A.Liskevich (Bristol)

MSC:

47D06	One-parameter semigroups and linear evolution equations
34G10	Linear differential equations in abstract spaces
93C25	Control/observation systems in abstract spaces
93D09	Robust stability
93D25	Input-output approaches in control theory

Keywords:

evolution semigroups; stability radius; exponential stability; spectral mapping theorem; infinite-dimensional linear control systems