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A Formal Proof in Coq of LaSalle’s Invariance Principle

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Interactive Theorem Proving (ITP 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10499))

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Abstract

Stability analysis of dynamical systems plays an important role in the study of control techniques. LaSalle’s invariance principle is a result about the asymptotic stability of the solutions to a nonlinear system of differential equations and several extensions of this principle have been designed to fit different particular kinds of system. In this paper we present a formalization, in the Coq proof assistant, of a slightly improved version of the original principle. This is a step towards a formal verification of dynamical systems.

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Notes

  1. 1.

    https://math-comp.github.io/math-comp/.

  2. 2.

    https://github.com/drouhling/LaSalle.

  3. 3.

    http://www.lix.polytechnique.fr/coq/pylons/contribs/view/Topology/v8.4.

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Acknowledgements

We thank the anonymous reviewers for their useful feedback.

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Authors and Affiliations

  1. Université Côte d’Azur, Inria, Sophia Antipolis, France

    Cyril Cohen & Damien Rouhling

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  1. Cyril Cohen
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  2. Damien Rouhling
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Correspondence to Cyril Cohen or Damien Rouhling .

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Editors and Affiliations

  1. University of Brasília, Brasília D.F., Brazil

    Mauricio Ayala-Rincón

  2. NASA, Hampton, VA, USA

    César A. Muñoz

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Cohen, C., Rouhling, D. (2017). A Formal Proof in Coq of LaSalle’s Invariance Principle. In: Ayala-Rincón, M., Muñoz, C.A. (eds) Interactive Theorem Proving. ITP 2017. Lecture Notes in Computer Science(), vol 10499. Springer, Cham. https://doi.org/10.1007/978-3-319-66107-0_10

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  • DOI: https://doi.org/10.1007/978-3-319-66107-0_10

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66106-3

  • Online ISBN: 978-3-319-66107-0

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