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Technical Brief

Further Comments on Taylor Series Expansion of the Delay/Advance Operator

[+] Author and Article Information
Eduardo García-Ramírez

Department of Electronics and Telecommunications,
Centro de Investigación Científica y de Educación Superior
de Ensenada, Ensenada,
Baja California 22860, Mexico
e-mail: eduardogar@protonmail.ch

Ollin Peñaloza-Mejía

Departamento de Ingeniería Eléctrica y Electrónica,
Instituto Tecnológico de Sonora,
Ciudad Obregón, Sonora 85130, Mexico
e-mail: ollin.penaloza@itson.edu.mx

Claude H. Moog

Institut de Recherche en Communications et Cybernétique
de Nantes,
UMR CNRS 6597,
Nantes Cedex 3, 44321, France
e-mail: moog@ieee.org

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received September 3, 2015; final manuscript received October 13, 2016; published online December 5, 2016. Assoc. Editor: Firdaus Udwadia.

J. Comput. Nonlinear Dynam 12(3), 034501 (Dec 05, 2016) (3 pages) Paper No: CND-15-1272; doi: 10.1115/1.4035058 History: Received September 03, 2015; Revised October 13, 2016

The limitations of the Taylor series approximations of the delayed variables have been documented by means of examples in several works. This note unifies these previous comments through a higher-level analysis of the issue. It is shown that the use of the truncated Taylor series expansion of the (inverse) advance operator does not feature the same drawbacks.

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References

Figures

Grahic Jump Location
Fig. 1

Zero to fourth order truncation systems response for Eq. (19), and the time-shifted delay system

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