Lyapunov stability analysis of higher-order 2-D systems

Authors:
C. Kojima;P. Rapisarda;K. Takaba
Affiliations:
Department of Information Physics and Computing, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo, Japan 113-0033;Information: Signals, Images, Systems group, School of Electronics and Computer Science, University of Southampton, Southampton, UK SO171BJ;Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, Japan 606---8501
Venue:
Multidimensional Systems and Signal Processing
Year:
2011

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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.