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

• DOI: 10.1016/j.sysconle.2005.04.015
• Publication Date: 2005-06-23T11:21:43Z
• Authors: B. Brogliato; A. Daniilidis; C. Lemaréchal; V. Acary
• Keywords: Differential inclusion; Complementarity (molecular biology); Dynamical system (definition)

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.