Convenient Model for Systems with Hystereses-Control

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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
Publication statusPublished - 2011
EventThe 50th IEEE Conference on Decision and Control and European Control Conference - Orlando, United States
Duration: 12 Dec 201115 Dec 2011


ConferenceThe 50th IEEE Conference on Decision and Control and European Control Conference
CountryUnited States


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