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

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.
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Bernard Brogliato, Aris Daniilidis, Claude Lemarechal, Vincent Acary. On the equivalence between complementarity systems, projected systems and differential inclusions. Systems and Control Letters, Elsevier, 2006, 55 (1), pp.45-51. ⟨10.1016/j.sysconle.2005.04.015⟩. ⟨inria-00423552⟩

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