Lyapunov stability analysis of higher-order 2D systems

Kojima, Chiaki, Rapisarda, Paolo and Takaba, Kiyotsugu (2010) Lyapunov stability analysis of higher-order 2D systems. Multidimensional Systems and Signal Processing, 22, 287-302.


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We prove a necessary and sufficient condition for the asymptotic stability of a 2D 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.

Item Type: Article
Keywords: 2D system, Lyapunov function, quadratic difference form, polynomial Lyapunov equation
Divisions : Faculty of Physical Sciences and Engineering > Electronics and Computer Science > Southampton Wireless Group
ePrint ID: 271388
Accepted Date and Publication Date:
Date Deposited: 12 Jul 2010 14:12
Last Modified: 31 Mar 2016 14:18
Further Information:Google Scholar

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