On the structural properties of the bounded control set of a linear control system

Víctor Ayala; Adriano Da Silva

doi:10.1007/s00030-022-00784-1

On the structural properties of the bounded control set of a linear control system

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Abstract

The present paper shows that the closure of the bounded control set of a linear control system contains all the bounded orbits of the system. As a consequence, we prove that the closure of this control set is the continuous image of the cartesian product of the set of control functions by the central subgroup associated with the drift of the system.

Original language	English
Article number	53
Journal	Nonlinear Differential Equations and Applications
Volume	29
Issue number	5
DOIs	https://doi.org/10.1007/s00030-022-00784-1
State	Published - Sep 2022

Keywords

Central subgroup
Control set
Linear systems
Periodic orbits

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10.1007/s00030-022-00784-1

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title = "On the structural properties of the bounded control set of a linear control system",

abstract = "The present paper shows that the closure of the bounded control set of a linear control system contains all the bounded orbits of the system. As a consequence, we prove that the closure of this control set is the continuous image of the cartesian product of the set of control functions by the central subgroup associated with the drift of the system.",

keywords = "Central subgroup, Control set, Linear systems, Periodic orbits",

author = "V{\'i}ctor Ayala and \{Da Silva\}, Adriano",

note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.",

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doi = "10.1007/s00030-022-00784-1",

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AU - Ayala, Víctor

AU - Da Silva, Adriano

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N2 - The present paper shows that the closure of the bounded control set of a linear control system contains all the bounded orbits of the system. As a consequence, we prove that the closure of this control set is the continuous image of the cartesian product of the set of control functions by the central subgroup associated with the drift of the system.

AB - The present paper shows that the closure of the bounded control set of a linear control system contains all the bounded orbits of the system. As a consequence, we prove that the closure of this control set is the continuous image of the cartesian product of the set of control functions by the central subgroup associated with the drift of the system.

KW - Central subgroup

KW - Control set

KW - Linear systems

KW - Periodic orbits

UR - https://www.scopus.com/pages/publications/85132415452

U2 - 10.1007/s00030-022-00784-1

DO - 10.1007/s00030-022-00784-1

M3 - Article

AN - SCOPUS:85132415452

SN - 1021-9722

VL - 29

JO - Nonlinear Differential Equations and Applications

JF - Nonlinear Differential Equations and Applications

IS - 5

M1 - 53

ER -

On the structural properties of the bounded control set of a linear control system

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