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International Workshop on Computer Algebra in Scientific Computing

CASC 2012: Computer Algebra in Scientific Computing pp 334–348Cite as

Verifiable Conditions on Asymptotic Stabilisability for a Class of Planar Switched Linear Systems

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7442))

Abstract

In this paper, we propose a computer algebra based approach for analyzing asymptotic stabilisability of a class of planar switched linear systems, where subsystems are assumed to be alternatively active. We start with an algebraizable sufficient condition on the existence of stabilizing switching lines and a multiple Lyapunov function. Then, we apply a real root classification based method to under-approximate this condition such that the under-approximation only involves the parametric coefficients. Afterward, we additionally use quantifier elimination to eliminate parameters in the multiple Lyapunov function, arriving at a quantifier-free formula over parameters in the switching lines. According to our intermediate under-approximation as well as our final quantifier-free formula, we can easily design explicit stabilizing switching laws. Moreover, based on a prototypical implementation, we use an illustrating example to show the applicability of our approach. Finally, the advantages of our approach are demonstrated by the comparisons with some related works in the literature.

This work was partly supported by NSFC-61003021 and SKLSDE-2011ZX-16.

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Author information

Authors and Affiliations

  1. SKLSDE, LMIB and School of Mathematics and Systems Science, Beihang University, Beijing, China

    Zhikun She & Haoyang Li

Authors
  1. Zhikun She
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  2. Haoyang Li
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Editor information

Editors and Affiliations

  1. Laboratory of Information Technologies (LIT), Joint Institute for Nuclear Research (JINR), 141980, Dubna, Russia

    Vladimir P. Gerdt

  2. Institut für Mathematik, Universität Kassel, Heinrich-Plett-Straße 40, 34132, Kassel, Germany

    Wolfram Koepf

  3. Institut für Informatik, Lehrstuhl für Effiziente Algorithmen, Technische Universität München, Boltzmannstraße 3, 85748, Garching, Germany

    Ernst W. Mayr

  4. Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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© 2012 Springer-Verlag Berlin Heidelberg

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She, Z., Li, H. (2012). Verifiable Conditions on Asymptotic Stabilisability for a Class of Planar Switched Linear Systems. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2012. Lecture Notes in Computer Science, vol 7442. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32973-9_28

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  • DOI: https://doi.org/10.1007/978-3-642-32973-9_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-32972-2

  • Online ISBN: 978-3-642-32973-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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