### Abstract

Original language | English |
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Place of Publication | Eindhoven |

Publisher | Technische Hogeschool Eindhoven |

Number of pages | 14 |

Publication status | Published - 1980 |

### Publication series

Name | Memorandum COSOR |
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Volume | 8009 |

ISSN (Print) | 0926-4493 |

### Fingerprint

### Cite this

*Asymptotic stability of a solution of an autonomous system in R2, consisting of subsystems*. (Memorandum COSOR; Vol. 8009). Eindhoven: Technische Hogeschool Eindhoven.

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*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.

Research output: Book/Report › Report › Academic

TY - BOOK

T1 - Asymptotic stability of a solution of an autonomous system in R2, consisting of subsystems

AU - Heuvel, van den, P.J.

PY - 1980

Y1 - 1980

N2 - 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.

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.

M3 - Report

T3 - Memorandum COSOR

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

PB - Technische Hogeschool Eindhoven

CY - Eindhoven

ER -