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Stability analysis of delay-differential equations by the method of steps and inverse Laplace transform

Abstract

It is demonstrated that the method of steps for linear delay-differential equation together with the inverse Laplace transform can be used to find a converging sequence of polynomial approximants to the transcendental function determining stability of the delay equation. Numerical stability charts are shown to illustrate convergence. This approach can serve as a basis for an efficient numerical method to determine stability regions for higher-order delay-differential equations

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Correspondence to Tamás Kalmár-Nagy.

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This paper is dedicated to the memory of professor Miklós Farkas, colleague and friend.

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Kalmár-Nagy, T. Stability analysis of delay-differential equations by the method of steps and inverse Laplace transform. Differ Equ Dyn Syst 17, 185–200 (2009). https://doi.org/10.1007/s12591-009-0014-x

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Keywords

  • Stability
  • Time-delay systems

Mathematics Subject Classification (2000)

  • 34K06
  • 34K20
  • 34K28