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.
|Journal||Systems and Control Letters|
|Publication status||Published - 1 Jan 2006|
- Complementarity systems
- Differential inclusions
- Hybrid dynamical systems
- Projected dynamics
- Unilateral dynamics