Evolution Semigroups and Stability of Time-Varying Systems on Banach Spaces

Author

T. Randolph
Yuri Latushkin
Stephen L. Clark, Missouri University of Science and TechnologyFollow

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 new 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.

Recommended Citation

T. Randolph et al., "Evolution Semigroups and Stability of Time-Varying Systems on Banach Spaces," Proceedings of the 36th IEEE Conference on Decision and Control (1997, San Diego, CA), vol. 4, pp. 3932 - 3937, Institute of Electrical and Electronics Engineers (IEEE), Dec 1997.

The definitive version is available at https://doi.org/10.1109/CDC.1997.652477

Department(s)

Mathematics and Statistics

Comments

Research of this author was supported by NSF DMS grant number 9622105.

Keywords and Phrases

Control system analysis; Mathematical models; State space methods; System stability; Banach spaces; Non autonomous systems; Stability radius; Time varying control systems

International Standard Book Number (ISBN)

978-0-7803-4187-2

International Standard Serial Number (ISSN)

0191-2216

Document Type

Article - Conference proceedings

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 1997 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

Publication Date

01 Dec 1997