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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 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.
2-D systems, Lyapunov stability, quadratic difference forms, four-variable polynomial algebra
Springer
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. In, Springer LNCIS. Springer. (In Press)

Record type: Book Section

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 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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Accepted/In Press date: 2010
Keywords: 2-D systems, Lyapunov stability, quadratic difference forms, four-variable polynomial algebra
Organisations: Southampton Wireless Group

Identifiers

Local EPrints ID: 268403
URI: http://eprints.soton.ac.uk/id/eprint/268403
PURE UUID: e61fc324-e626-494d-9b9d-e2cdf1a4f8f7

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Date deposited: 21 Jan 2010 11:02
Last modified: 14 Mar 2024 09:09

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Contributors

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

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