Evolution semigroups and stability of time-varying systems on Banach spaces

Author

Randolph, T. ; Latushkin, Y. ; Clark, S.

Author_Institution

Math., Missouri Univ., Rolla, MO, USA

Volume

4

fYear

1997

fDate

10-12 Dec 1997

Firstpage

3932

Abstract

The two main topics addressed are: (i) the relationship between internal, external, and input-output stability, and (ii) stability of time-invariant systems including a Banach-space formula for the stability radius. With regard to (i), we show that a nonautonomous system is internally stable if and only if it is stabilizable, detectable and input-output stable; the short proof seems to be new even for finite-dimensional autonomous systems. For (ii), new formulas are given, in terms of the coefficients of the system, for the L_p-norm of the input-output operator and for the stability radius of the system

Keywords

Banach spaces; asymptotic stability; group theory; input-output stability; multidimensional systems; time-varying systems; Banach spaces; evolution semigroups; external stability; finite-dimensional autonomous systems; input-output operator; input-output stability; internal stability; nonautonomous system; stability radius; time-invariant systems; time-varying systems; Convergence; Differential equations; Ear; Hilbert space; Mathematics; Partial differential equations; Stability analysis; Stress; Time varying systems; Topology;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 1997., Proceedings of the 36th IEEE Conference on

Conference_Location

San Diego, CA

ISSN

0191-2216

Print_ISBN

0-7803-4187-2

Type

conf

DOI

10.1109/CDC.1997.652477

Filename

652477