On the equivalence between complementarity systems, projected systems and differential inclusions

B. Brogliato; A. Daniilidis; C. Lemaréchal; V. Acary

doi:https://doi.org/10.1016/j.sysconle.2005.04.015

On the equivalence between complementarity systems, projected systems and differential inclusions

B. Brogliato, A. Daniilidis, C. Lemaréchal, V. Acary

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

92 Citations (Scopus)

Abstract

In this note, we prove the equivalence, under appropriate conditions, between several dynamical formalisms: projected dynamical systems, two types of differential inclusions, and a class of complementarity dynamical systems. Each of these dynamical systems can also be considered as a hybrid dynamical system. This work both generalizes previous results and sheds some new light on the relationship between known formalisms; besides, it exclusively uses tools from convex analysis. © 2005 Elsevier B.V. All rights reserved.

Original language	English
Pages (from-to)	45-51
Journal	Systems and Control Letters
Volume	55
DOIs	https://doi.org/10.1016/j.sysconle.2005.04.015
Publication status	Published - 1 Jan 2006

Keywords

Complementarity systems
Differential inclusions
Hybrid dynamical systems
Projected dynamics
Unilateral dynamics

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AU - Lemaréchal, C.

AU - Acary, V.

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N2 - In this note, we prove the equivalence, under appropriate conditions, between several dynamical formalisms: projected dynamical systems, two types of differential inclusions, and a class of complementarity dynamical systems. Each of these dynamical systems can also be considered as a hybrid dynamical system. This work both generalizes previous results and sheds some new light on the relationship between known formalisms; besides, it exclusively uses tools from convex analysis. © 2005 Elsevier B.V. All rights reserved.

AB - In this note, we prove the equivalence, under appropriate conditions, between several dynamical formalisms: projected dynamical systems, two types of differential inclusions, and a class of complementarity dynamical systems. Each of these dynamical systems can also be considered as a hybrid dynamical system. This work both generalizes previous results and sheds some new light on the relationship between known formalisms; besides, it exclusively uses tools from convex analysis. © 2005 Elsevier B.V. All rights reserved.

KW - Complementarity systems

KW - Differential inclusions

KW - Hybrid dynamical systems

KW - Projected dynamics

KW - Unilateral dynamics

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