Convenient Model for Systems with Hystereses-Control

Research output: Contribution to journalConference article in JournalResearchpeer-review

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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 languageEnglish
JournalI E E E Conference on Decision and Control. Proceedings
Pages (from-to)6140-6145
Number of pages6
ISSN0743-1546
DOIs
Publication statusPublished - 2011
EventThe 50th IEEE Conference on Decision and Control and European Control Conference - Orlando, United States
Duration: 12 Dec 201115 Dec 2011

Conference

ConferenceThe 50th IEEE Conference on Decision and Control and European Control Conference
CountryUnited States
CityOrlando
Period12/12/201115/12/2011

Fingerprint

Hysteresis
Polyhedral Sets
Dynamical systems
Dynamical system
Switched Systems
Closed Orbit
Affine Systems
Smooth Manifold
Cartesian product
Chart
Facet
Euclidean space
Stability Analysis
Torus
Disjoint
State Space
Orbits
Differential equations
Fixed point
Model

Cite this

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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",

}

Convenient Model for Systems with Hystereses-Control. / Wisniewski, Rafal; Leth, John-Josef.

In: I E E E Conference on Decision and Control. Proceedings, 2011, p. 6140-6145.

Research output: Contribution to journalConference article in JournalResearchpeer-review

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

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

SN - 0743-1546

ER -