ESTONIAN ACADEMY
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eesti teaduste
akadeemia kirjastus
PUBLISHED
SINCE 1952
 
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proceedings
of the estonian academy of sciences
ISSN 1736-7530 (Electronic)
ISSN 1736-6046 (Print)
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Theorem on the differentiation of a composite function with a vector argument; pp. 195–200
PDF | doi: 10.3176/proc.2010.3.01

Authors
Vadim Kaparin ORCID Icon, Ülle Kotta ORCID Icon
Abstract

The paper provides a theorem on the differentiation of a composite function with a vector argument. The theorem shows how the partial derivative of the total derivative of the composite function can be expressed through the total derivative of the partial derivative of the composite function. The proof of the theorem is based on Mishkov’s formula, which is the generalization of the well-known Faà di Bruno’s formula for a composite function with a vector argument.

References

1. Johnson, W. P. The curious history of Faa di Bruno’s Formula. Amer. Math. Monthly, 2002, 109, 217–234.
doi:10.2307/2695352

2. Kaparin, V. and Kotta, Ü. Necessary and sufficient conditions in terms of differential-forms for linearization of the state equations up to input-output injections. UKACC International Conference on CONTROL 2010 7–10 September, Coventry, UK (submitted for publication).

3. Mishkov, R. L. Generalization of the formula of Faa di Bruno for a composite function with a vector argument. Internat. J. Math. Math. Sci., 2000, 24(7), 481–491.
doi:10.1155/S0161171200002970


4. Mishkov, R. L. Nonlinear observer design by reduced generalized observer canonical form. Internat. J. Control, 2005, 78, 172–185.doi:10.1080/00207170500073806

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