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Iterative Construction of Complete Lyapunov Functions: Analysis of Algorithm Efficiency

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Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH 2018)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 947))

Abstract

Differential equations describe many interesting phenomena arising from various disciplines. This includes many important models, e.g. predator-prey in population biology or the Van der Pol oscillator in electrical engineering. Complete Lyapunov functions allow for the systematic study of the qualitative behaviour of complicated systems. In this paper, we extend the analysis of the algorithm presented in [1]. We study the efficiency of our algorithm and discuss important sections of the code.

The first author in this paper is supported by the Icelandic Research Fund (Rannís) grant number 163074-052, Complete Lyapunov functions: Efficient numerical computation.

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References

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Acknowledgement

First author wants to thank Dr. A. Argáez for nice discussions on normed spaces as well as the Icelandic Research Fund (Rannís) for funding this work under the grant: number 163074-052, Complete Lyapunov functions: Efficient numerical computation.

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Authors and Affiliations

  1. Science Institute, University of Iceland, Dunhagi 3, 107, Reykjavík, Iceland

    Carlos Argáez & Sigurdur Hafstein

  2. Department of Mathematics, University of Sussex, Falmer, Brighton, BN1 9QH, UK

    Peter Giesl

Authors
  1. Carlos Argáez
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  2. Peter Giesl
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  3. Sigurdur Hafstein
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Corresponding author

Correspondence to Carlos Argáez .

Editor information

Editors and Affiliations

  1. King Abdullah II School of Information Technology, University of Jordan, Amman, Jordan

    Mohammad S. Obaidat

  2. School of Electrical Engineering and Computer Science, University of Ottawa, Ottawa, ON, Canada

    Tuncer Ören

  3. University of Calabria, Rende, Cosenza, Italy

    Floriano De Rango

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Argáez, C., Giesl, P., Hafstein, S. (2020). Iterative Construction of Complete Lyapunov Functions: Analysis of Algorithm Efficiency. In: Obaidat, M., Ören, T., Rango, F. (eds) Simulation and Modeling Methodologies, Technologies and Applications. SIMULTECH 2018. Advances in Intelligent Systems and Computing, vol 947. Springer, Cham. https://doi.org/10.1007/978-3-030-35944-7_5

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