It is known that stability properties of delay-differential equations are not preserved by Taylor series expansion of the delayed term. Still, this technique is often used to approximate delayed systems by ordinary differential equations in different engineering and biological applications. In this brief, it is demonstrated through some simple second-order scalar systems that low-order Taylor series expansion of the delayed term approximates the asymptotic behavior of the original delayed system only for certain parameter regions, while for high-order expansions, the approximate system is unstable independently of the system parameters.
On the Approximation of Delayed Systems by Taylor Series Expansion
Contributed by the Design Engineering Division of ASME for publication in the Journal of Computational and Nonlinear Dynamics. Manuscript received December 31, 2013; final manuscript received March 12, 2014; published online January 12, 2015. Assoc. Editor: Parviz Nikravesh.
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Insperger, T. (March 1, 2015). "On the Approximation of Delayed Systems by Taylor Series Expansion." ASME. J. Comput. Nonlinear Dynam. March 2015; 10(2): 024503. https://doi.org/10.1115/1.4027180
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