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Title: Stability and boundedness of controllable continuous flows (English)
Author: Tumajer, František
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 33
Issue: 6
Year: 1988
Pages: 493-504
Summary lang: English
Summary lang: Russian
Summary lang: Czech
Category: math
Summary: In the paper the concept of a controllable continuous flow in a metric space is introduced as a generalization of a controllable system of differential equations in a Banach space, and various kinds of stability and of boundedness of this flow are defined. Theorems stating necessary and sufficient conditions for particular kinds of stability and boundedness are formulated in terms of Ljapunov functions. (English)
Keyword: uniform stability of a set with respect to a flow
Keyword: uniform boundedness of a flow with respect to a set
Keyword: controllable continuous flow
Keyword: controllable system of differential equations
MSC: 34D20
MSC: 34D99
MSC: 34H05
MSC: 47H20
MSC: 58F25
MSC: 93C15
MSC: 93D05
idZBL: Zbl 0659.34058
idMR: MR0973243
DOI: 10.21136/AM.1988.104327
Date available: 2008-05-20T18:35:43Z
Last updated: 2020-07-28
Stable URL:
Reference: [1] J. Dieudonné: Foundations of modem analysis.Academic Press, New York-London 1960. Russian translation: Mir, Moscow, 1964. MR 0120319
Reference: [2] F. Tumajer: Uniform stability and uniform asymptotic stability of sets with respect to a continuous flow.(Czech.) Časopis pěst. mat. 97 (1972), 86-93. Zbl 0235.34103, MR 0306650
Reference: [3] F. Tumajer: Ljapunov's method in the theory of boundedness of linear controlled flows.(Czech.) Časopis pěst. mat. 98 (1973), 278-284. MR 0326094


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