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Liapunov’s Second Method and the Invariance Principle

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The Convergence Problem for Dissipative Autonomous Systems

Part of the book series: SpringerBriefs in Mathematics ((BRIEFSMATH))

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Abstract

We introduce Liapunov functions and make a gradual transition from Liapunov’s second method to the general Barbashin-Krasovskii-LaSalle invariance principle. The main underlying idea is that conservation of the Liapunov function throughout a positive trajectory is usually possible only for special initial states. In particular, if a dynamical system has a strict Liapunov function, it is gradient-like. We apply these concepts to stability and convergence, with application to typical examples.

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References

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Authors and Affiliations

  1. Laboratoire Jacques-Louis Lions, Sorbonne Universités, UPMC Univ Paris 06, CNRS, UMR 7598, 4, place Jussieu, 75005, Paris, France

    Alain Haraux

  2. Institut Préparatoire aux Etudes Scientifiques et Techniques, Université de Carthage, B.P. 51, 2070, La Marsa, Tunisia

    Mohamed Ali Jendoubi

  3. Faculté des sciences de Tunis, Laboratoire EDP-LR03ES04, Université de Tunis El Manar, Tunis, Tunisia

    Mohamed Ali Jendoubi

Authors
  1. Alain Haraux
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  2. Mohamed Ali Jendoubi
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Correspondence to Alain Haraux .

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Haraux, A., Jendoubi, M. (2015). Liapunov’s Second Method and the Invariance Principle. In: The Convergence Problem for Dissipative Autonomous Systems. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-23407-6_8

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