High order approximation of implicitly defined maps

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Abstract

Approximations for the function φ{symbol} implicitly defined by φ{symbol}(u)=Φ(u, φ{symbol}(u)) are obtained via the iterative scheme φ{symbol}n(u)=Φ(u, φ{symbol}n-1(u)). In this paper the uniform convergence of high order derivatives of φ{symbol}n to the corresponding derivatives of φ{symbol} is proved. This result yields a high order approximation theorem for the input-output map generated by a nonlinear control system, using linear combinations of iterated integrals of the control.

Original languageEnglish (US)
Pages (from-to)163-173
Number of pages11
JournalAnnali di Matematica Pura ed Applicata
Volume137
Issue number1
DOIs
StatePublished - Dec 1 1984

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

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