Asymptotic stability of a solution of an autonomous system in R2, consisting of subsystems

P.J. Heuvel, van den

Research output: Book/ReportReportAcademic

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Abstract

In this paper a generalization is proved of a theorem by Laroque (1979). This theorem asserts that if an autonomous system x = F(x) consists of linear subsystems defined on cones in R2 and if the function F(x) is continuous, then the origin is an asymptotically stable solution of the system, if the subsystems are asymptotically stable in R2. It is shown that the linearity restrictions in the theorem of Laroque can be relaxed in a neighbourhood of the equilibrium.
Original languageEnglish
Place of PublicationEindhoven
PublisherTechnische Hogeschool Eindhoven
Number of pages14
Publication statusPublished - 1980

Publication series

NameMemorandum COSOR
Volume8009
ISSN (Print)0926-4493

Fingerprint

Autonomous Systems
Asymptotic Stability
Subsystem
Asymptotically Stable
Theorem
Stable Solution
Linearity
Cone
Restriction

Cite this

Heuvel, van den, P. J. (1980). Asymptotic stability of a solution of an autonomous system in R2, consisting of subsystems. (Memorandum COSOR; Vol. 8009). Eindhoven: Technische Hogeschool Eindhoven.
Heuvel, van den, P.J. / Asymptotic stability of a solution of an autonomous system in R2, consisting of subsystems. Eindhoven : Technische Hogeschool Eindhoven, 1980. 14 p. (Memorandum COSOR).
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Heuvel, van den, PJ 1980, Asymptotic stability of a solution of an autonomous system in R2, consisting of subsystems. Memorandum COSOR, vol. 8009, Technische Hogeschool Eindhoven, Eindhoven.

Asymptotic stability of a solution of an autonomous system in R2, consisting of subsystems. / Heuvel, van den, P.J.

Eindhoven : Technische Hogeschool Eindhoven, 1980. 14 p. (Memorandum COSOR; Vol. 8009).

Research output: Book/ReportReportAcademic

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AB - In this paper a generalization is proved of a theorem by Laroque (1979). This theorem asserts that if an autonomous system x = F(x) consists of linear subsystems defined on cones in R2 and if the function F(x) is continuous, then the origin is an asymptotically stable solution of the system, if the subsystems are asymptotically stable in R2. It is shown that the linearity restrictions in the theorem of Laroque can be relaxed in a neighbourhood of the equilibrium.

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Heuvel, van den PJ. Asymptotic stability of a solution of an autonomous system in R2, consisting of subsystems. Eindhoven: Technische Hogeschool Eindhoven, 1980. 14 p. (Memorandum COSOR).