Evolution Semigroups and Stability of Time-Varying Systems on Banach Spaces
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 Lp-norm of the input-output operator and for the stability radius of the system.
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
Mathematics and Statistics
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)
International Standard Serial Number (ISSN)
Article - Conference proceedings
© 1997 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.
01 Dec 1997