Convenient Model for Systems with Hystereses-Control

Rafal Wisniewski; John-Josef Leth

doi:10.1109/CDC.2011.6161090

Convenient Model for Systems with Hystereses-Control

Rafal Wisniewski, John-Josef Leth

Research output: Contribution to journal › Conference article in Journal › Research › peer-review

3 Citations (Scopus)

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Abstract

We establish a model of a system with hystereses, which allows for
standard stability analysis of fixed points and closed orbits. To
this end, we represent a system with hystereses as a
piecewise-affine switched system that consists of a family of
dynamical systems defined on disjoint polyhedral sets. The discrete
transitions are realized by reset maps defined on the facets of
these polyhedral sets. We have shown that the state space of a
resulting switched system is a smooth manifold, the Cartesian
product of a torus with an Euclidean space. Additionally, we
construct the charts explicitly. Thereby, the analysis of a system
with hystereses can be seen as the analysis of a dynamical system on
a manifold, locally in chars. This dynamical system corresponds to
a differential equation with discontinuous right hand side which
solution is shown to exist and to be unique.

Original language	English
Journal	I E E E Conference on Decision and Control. Proceedings
Pages (from-to)	6140-6145
Number of pages	6
ISSN	0743-1546
DOIs	https://doi.org/10.1109/CDC.2011.6161090
Publication status	Published - 2011
Event	The 50th IEEE Conference on Decision and Control and European Control Conference - Orlando, United States Duration: 12 Dec 2011 → 15 Dec 2011

Conference

Conference	The 50th IEEE Conference on Decision and Control and European Control Conference
Country/Territory	United States
City	Orlando
Period	12/12/2011 → 15/12/2011

Access to Document

10.1109/CDC.2011.6161090

MultiHysteresisCDCAccepted author manuscript, 144 KB

http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6161090

AUB Link

Search for the material in Aalborg University Library's search engine

Hybrid Control
Leth, J. & Wisniewski, R.
The Danish Council for Technology and Innovation
01/03/2008 → 31/12/2011
Project: Research

Cite this

@inproceedings{f18aac26518d4e93badccc0e8a8398b4,

title = "Convenient Model for Systems with Hystereses-Control",

abstract = " We establish a model of a system with hystereses, which allows for standard stability analysis of fixed points and closed orbits. To this end, we represent a system with hystereses as a piecewise-affine switched system that consists of a family of dynamical systems defined on disjoint polyhedral sets. The discrete transitions are realized by reset maps defined on the facets of these polyhedral sets. We have shown that the state space of a resulting switched system is a smooth manifold, the Cartesian product of a torus with an Euclidean space. Additionally, we construct the charts explicitly. Thereby, the analysis of a system with hystereses can be seen as the analysis of a dynamical system on a manifold, locally in chars. This dynamical system corresponds to a differential equation with discontinuous right hand side which solution is shown to exist and to be unique.",

author = "Rafal Wisniewski and John-Josef Leth",

year = "2011",

doi = "10.1109/CDC.2011.6161090",

language = "English",

pages = "6140--6145",

journal = "I E E E Conference on Decision and Control. Proceedings",

issn = "0743-1546",

publisher = "IEEE Computer Society Press",

note = "The 50th IEEE Conference on Decision and Control and European Control Conference ; Conference date: 12-12-2011 Through 15-12-2011",

}

TY - GEN

T1 - Convenient Model for Systems with Hystereses-Control

AU - Wisniewski, Rafal

AU - Leth, John-Josef

PY - 2011

Y1 - 2011

N2 - We establish a model of a system with hystereses, which allows for standard stability analysis of fixed points and closed orbits. To this end, we represent a system with hystereses as a piecewise-affine switched system that consists of a family of dynamical systems defined on disjoint polyhedral sets. The discrete transitions are realized by reset maps defined on the facets of these polyhedral sets. We have shown that the state space of a resulting switched system is a smooth manifold, the Cartesian product of a torus with an Euclidean space. Additionally, we construct the charts explicitly. Thereby, the analysis of a system with hystereses can be seen as the analysis of a dynamical system on a manifold, locally in chars. This dynamical system corresponds to a differential equation with discontinuous right hand side which solution is shown to exist and to be unique.

AB - We establish a model of a system with hystereses, which allows for standard stability analysis of fixed points and closed orbits. To this end, we represent a system with hystereses as a piecewise-affine switched system that consists of a family of dynamical systems defined on disjoint polyhedral sets. The discrete transitions are realized by reset maps defined on the facets of these polyhedral sets. We have shown that the state space of a resulting switched system is a smooth manifold, the Cartesian product of a torus with an Euclidean space. Additionally, we construct the charts explicitly. Thereby, the analysis of a system with hystereses can be seen as the analysis of a dynamical system on a manifold, locally in chars. This dynamical system corresponds to a differential equation with discontinuous right hand side which solution is shown to exist and to be unique.

U2 - 10.1109/CDC.2011.6161090

DO - 10.1109/CDC.2011.6161090

M3 - Conference article in Journal

SN - 0743-1546

SP - 6140

EP - 6145

JO - I E E E Conference on Decision and Control. Proceedings

JF - I E E E Conference on Decision and Control. Proceedings

T2 - The 50th IEEE Conference on Decision and Control and European Control Conference

Y2 - 12 December 2011 through 15 December 2011

ER -

Convenient Model for Systems with Hystereses-Control

Abstract

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Projects

Hybrid Control

Cite this