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A state-space temporal finite element approach for stability investigations of delay equations

Publication ,  Journal Article
Khasawneh, FA; Mann, BP; Patel, B
Published in: Proceedings of the ASME Conference on Smart Materials, Adaptive Structures and Intelligent Systems 2009, SMASIS2009
December 1, 2009

This paper describes a new approach to examine the stability of delay differential equations that builds upon prior work using temporal finite element analysis. In contrast to previous analyses, which could only be applied to second order delay differential equations, the present manuscript develops an approach which can be applied to a broader class of systems - systems that may be written in the form of a state space model. A primary outcome from this work is a generalized framework to investigate the asymptotic stability of autonomous delay differential equations with a single time delay. Furthermore, this approach is shown to be applicable to time-periodic delay differential equations and equations that are piecewise continuous. Copyright © 2009 by ASME.

Duke Scholars

Published In

Proceedings of the ASME Conference on Smart Materials, Adaptive Structures and Intelligent Systems 2009, SMASIS2009

DOI

Publication Date

December 1, 2009

Volume

1

Start / End Page

415 / 423
 

Citation

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Khasawneh, F. A., Mann, B. P., & Patel, B. (2009). A state-space temporal finite element approach for stability investigations of delay equations. Proceedings of the ASME Conference on Smart Materials, Adaptive Structures and Intelligent Systems 2009, SMASIS2009, 1, 415–423. https://doi.org/10.1115/SMASIS2009-1263
Khasawneh, F. A., B. P. Mann, and B. Patel. “A state-space temporal finite element approach for stability investigations of delay equations.” Proceedings of the ASME Conference on Smart Materials, Adaptive Structures and Intelligent Systems 2009, SMASIS2009 1 (December 1, 2009): 415–23. https://doi.org/10.1115/SMASIS2009-1263.
Khasawneh FA, Mann BP, Patel B. A state-space temporal finite element approach for stability investigations of delay equations. Proceedings of the ASME Conference on Smart Materials, Adaptive Structures and Intelligent Systems 2009, SMASIS2009. 2009 Dec 1;1:415–23.
Khasawneh, F. A., et al. “A state-space temporal finite element approach for stability investigations of delay equations.” Proceedings of the ASME Conference on Smart Materials, Adaptive Structures and Intelligent Systems 2009, SMASIS2009, vol. 1, Dec. 2009, pp. 415–23. Scopus, doi:10.1115/SMASIS2009-1263.
Khasawneh FA, Mann BP, Patel B. A state-space temporal finite element approach for stability investigations of delay equations. Proceedings of the ASME Conference on Smart Materials, Adaptive Structures and Intelligent Systems 2009, SMASIS2009. 2009 Dec 1;1:415–423.

Published In

Proceedings of the ASME Conference on Smart Materials, Adaptive Structures and Intelligent Systems 2009, SMASIS2009

DOI

Publication Date

December 1, 2009

Volume

1

Start / End Page

415 / 423