Switching, relay and complementarity systems: A tutorial on their well-posedness and relationships

Carmina Georgescu 1 Bernard Brogliato 1 Vincent Acary 1, *
* Corresponding author
1 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : This paper reviews the relationships between switching systems defined from a partition of the state space into convex cells, and relay or complementarity dynamical systems, which are other classes of discontinuous systems. Well-posedness results (i.e. results on the existence and the uniqueness of solutions) for different classes of relay and complementarity systems which are also switching systems are presented. The reverse issue (when can a switching system be rewritten equivalently as a relay or a complementarity system) is also tackled. Many examples from Mechanics, Circuits, and Biology illustrate the developments throughout the paper. The paper focuses on systems with continuous solutions (i.e. with no state jumps). Convexity is the central property.
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Carmina Georgescu, Bernard Brogliato, Vincent Acary. Switching, relay and complementarity systems: A tutorial on their well-posedness and relationships. Physica D: Nonlinear Phenomena, Elsevier, 2012, Dynamics and Bifurcations of Nonsmooth Systems, 241 (22), pp.50. ⟨http://www.sciencedirect.com/science/article/pii/S0167278911002934⟩. ⟨10.1016/j.physd.2011.10.014⟩. ⟨hal-00646982⟩

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