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Lyapunov Stability Analysis of Higher-Order 2-D Systems

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Perspectives in Mathematical System Theory, Control, and Signal Processing

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 398))

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Abstract

We prove a necessary and sufficient condition for the asymptotic stability of a 2-D system described by a system of higher-order linear partial difference equations. We use the definition of asymptotic stability given by Valcher in “Characteristic Cones and Stability Properties of Two-Dimensional Autonomous Behaviors”, IEEE Trans. Circ. Syst. — Part I: Fundamental Theory and Applications, vol. 47, no. 3, pp. 290-302, 2000. This property is shown to be equivalent to the existence of a vector Lyapunov functional satisfying certain positivity conditions together with its divergence along the system trajectories. We use the behavioral framework and the calculus of quadratic difference forms based on four variable polynomial algebra.

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Author information

Authors and Affiliations

  1. Department of Information Physics and Computing, Graduate School of Information Science and Technology, The University of Tokyo, Hongo, Bunkyo-Ku, Tokyo, 113-0033, Japan

    Chiaki Kojima

  2. Information: Signals, Images, Systems group, School of Electronics and Computer Science, University of Southampton, SO171BJ, Southampton, United Kingdom

    Paolo Rapisarda

  3. Dept. of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, 606–8501, Japan

    Kiyotsugu Takaba

Authors
  1. Chiaki Kojima
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  2. Paolo Rapisarda
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  3. Kiyotsugu Takaba
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Editor information

Editors and Affiliations

  1. ESAT, K.U.Leuven, Kasteelpark Arenberg 10, 3001, Leuven, Belgium

    Jan C. Willems

  2. Department of Information Physics and Computing, Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, 113-8656, Tokyo, Japan

    Shinji Hara

  3. Control Systems Theory Group, Department of Applied Mathematics and Physics , Graduate School of Informatics, Kyoto University, Yoshida-honmachi, 606-8501, Kyoto, Japan

    Yoshito Ohta

  4. Dept. Applied Analysis & Complex Dynamic Systems, Kyoto University, 606-8501, Kyoto, Japan

    Hisaya Fujioka

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Kojima, C., Rapisarda, P., Takaba, K. (2010). Lyapunov Stability Analysis of Higher-Order 2-D Systems. In: Willems, J.C., Hara, S., Ohta, Y., Fujioka, H. (eds) Perspectives in Mathematical System Theory, Control, and Signal Processing. Lecture Notes in Control and Information Sciences, vol 398. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-93918-4_18

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  • DOI: https://doi.org/10.1007/978-3-540-93918-4_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-93917-7

  • Online ISBN: 978-3-540-93918-4

  • eBook Packages: EngineeringEngineering (R0)

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