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Generic Singularities of Relay Systems

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Abstract

We discuss a class of nonsmooth vector fields on \(\mathbb{R}^{4}\) which are called relay systems. The main result provides a systematic classification of typical singularities which arise in generic one-parameter families of such systems. This is done by means of the notion of the mild equivalence between two relay systems. The theory is used to give a geometric characterization of the phase space in neighborhoods of the singularities, and tools of the singularity theory play a key role.

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Authors and Affiliations

  1. IMB, UMR CNRS 5584, Université de Bourgogne, Dijon, France

    A. Jacquemard

  2. Faculdade de Matemática, Federal University of Uberlândia, Uberlândia, MG, Brasil

    W. F. Pereira

  3. Instituto de Matemática e Estatística, University of Campinas, Campinas, SP, Brasil

    M. A. Teixeira

Authors
  1. A. Jacquemard
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  2. W. F. Pereira
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  3. M. A. Teixeira
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Correspondence to A. Jacquemard.

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Jacquemard, A., Pereira, W.F. & Teixeira, M.A. Generic Singularities of Relay Systems. J Dyn Control Syst 13, 503–530 (2007). https://doi.org/10.1007/s10883-007-9028-2

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  • DOI: https://doi.org/10.1007/s10883-007-9028-2

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