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Lyapunov stability analysis of higher-order 2-D systems

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Abstract

In this paper 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 show that asymptotic stability is 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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Authors and Affiliations

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

    C. Kojima

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

    P. Rapisarda

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

    K. Takaba

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  1. C. Kojima
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  2. P. Rapisarda
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  3. K. Takaba
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Correspondence to C. Kojima.

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Kojima, C., Rapisarda, P. & Takaba, K. Lyapunov stability analysis of higher-order 2-D systems. Multidim Syst Sign Process 22, 287–302 (2011). https://doi.org/10.1007/s11045-010-0124-1

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  • DOI: https://doi.org/10.1007/s11045-010-0124-1

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