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Lyapunov stability analysis of higher-order 2D systems

Lyapunov stability analysis of higher-order 2D systems
Lyapunov stability analysis of higher-order 2D systems
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.
2D system, Lyapunov function, quadratic difference form, polynomial Lyapunov equation
287-302
Kojima, Chiaki
0a50491d-140e-49cd-a257-2816cf504880
Rapisarda, Paolo
79efc3b0-a7c6-4ca7-a7f8-de5770a4281b
Takaba, Kiyotsugu
951ed1dd-9ead-4dad-bb6f-093c68f52052
Kojima, Chiaki
0a50491d-140e-49cd-a257-2816cf504880
Rapisarda, Paolo
79efc3b0-a7c6-4ca7-a7f8-de5770a4281b
Takaba, Kiyotsugu
951ed1dd-9ead-4dad-bb6f-093c68f52052

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

Record type: Article

Abstract

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.

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Published date: 2010
Keywords: 2D system, Lyapunov function, quadratic difference form, polynomial Lyapunov equation
Organisations: Southampton Wireless Group

Identifiers

Local EPrints ID: 271388
URI: http://eprints.soton.ac.uk/id/eprint/271388
PURE UUID: e17ae170-0552-4296-8ba8-aa86cc01d2eb

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Date deposited: 12 Jul 2010 14:12
Last modified: 14 Mar 2024 09:30

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Contributors

Author: Chiaki Kojima
Author: Paolo Rapisarda
Author: Kiyotsugu Takaba

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