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Stability of Delay Equations Written as State Space Models

Publication ,  Journal Article
Mann, BP; Patel, BR
Published in: JOURNAL OF VIBRATION AND CONTROL
June 2010

In this paper we describe 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.

Duke Scholars

Published In

JOURNAL OF VIBRATION AND CONTROL

DOI

ISSN

1077-5463

Publication Date

June 2010

Volume

16

Issue

7-8, SI

Start / End Page

1067 / 1085

Related Subject Headings

  • Acoustics
  • 4017 Mechanical engineering
  • 4005 Civil engineering
  • 0913 Mechanical Engineering
  • 0906 Electrical and Electronic Engineering
 

Citation

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Mann, B. P., & Patel, B. R. (2010). Stability of Delay Equations Written as State Space Models. JOURNAL OF VIBRATION AND CONTROL, 16(7–8, SI), 1067–1085. https://doi.org/10.1177/1077546309341111
Mann, B. P., and B. R. Patel. “Stability of Delay Equations Written as State Space Models.” JOURNAL OF VIBRATION AND CONTROL 16, no. 7–8, SI (June 2010): 1067–85. https://doi.org/10.1177/1077546309341111.
Mann BP, Patel BR. Stability of Delay Equations Written as State Space Models. JOURNAL OF VIBRATION AND CONTROL. 2010 Jun;16(7–8, SI):1067–85.
Mann, B. P., and B. R. Patel. “Stability of Delay Equations Written as State Space Models.” JOURNAL OF VIBRATION AND CONTROL, vol. 16, no. 7–8, SI, June 2010, pp. 1067–85. Manual, doi:10.1177/1077546309341111.
Mann BP, Patel BR. Stability of Delay Equations Written as State Space Models. JOURNAL OF VIBRATION AND CONTROL. 2010 Jun;16(7–8, SI):1067–1085.
Journal cover image

Published In

JOURNAL OF VIBRATION AND CONTROL

DOI

ISSN

1077-5463

Publication Date

June 2010

Volume

16

Issue

7-8, SI

Start / End Page

1067 / 1085

Related Subject Headings

  • Acoustics
  • 4017 Mechanical engineering
  • 4005 Civil engineering
  • 0913 Mechanical Engineering
  • 0906 Electrical and Electronic Engineering