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

PHYSICA D-NONLINEAR PHENOMENA

卷:241

Article

Georgescu, Carmina¹  Brogliato, Bernard¹  Acary, Vincent¹ 

[1] INRIA, BIPOP Team Project, 655 Ave Europe, F-38330 Montbonnot St Martin, France

关键词: Discontinuous systems;    Relay systems;    Complementarity systems;    Piecewise linear systems;    Multivalued systems;    Filippov systems;   

DOI  :  10.1016/j.physd.2011.10.014

来源: Elsevier

【 摘 要 】

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. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free