TY - CONF

T1 - Convenient Model for Systems with Hystereses-Control

A1 - Wisniewski,Rafal

A1 - Leth,John-Josef

AU - Wisniewski,Rafal

AU - Leth,John-Josef

PB - I E E E I E E E Control Systems Society

PY - 2011

Y1 - 2011

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

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

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

U2 - 10.1109/CDC.2011.6161090

DO - 10.1109/CDC.2011.6161090

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

SP - 6140

EP - 6145

ER -