Further comments on Taylor series expansion of the delay/advance operator

Eduardo Garcia-Ramirez (1) , Ollin Peñaloza-Mejia (2) , Claude H. Moog (3)

1 CICESE - Centro de Investigacion Cientifica y de Education Superior de Ensenada [Mexico]
2 Electrical and Electronics Departement (Instituto Tecnológico de Sonora (ITSON))
3 LS2N - Laboratoire des Sciences du Numérique de Nantes

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. First, a general negative result is derived for the use of higher order truncation of the Taylor series. It covers the properties of the special examples in the literature. Second, it is shown that the use of the truncated Taylor series expansion of the (inverse) advance operator does not feature similar drawbacks and may be efficient in practice, depending on the system parameters.

Mots clés: time-delay; Taylor series; timedelay feedback; stability

Domaines: Automatique

Eduardo Garcia-Ramirez, Ollin Peñaloza-Mejia, Claude H. Moog. Further comments on Taylor series expansion of the delay/advance operator. Journal of Computational and Nonlinear Dynamics, 2017, 12 (3), pp.034501-3. ⟨10.1115/1.4035058⟩. ⟨hal-01374775⟩