### 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 language | English (US) |
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Pages (from-to) | 163-173 |

Number of pages | 11 |

Journal | Annali di Matematica Pura ed Applicata |

Volume | 137 |

Issue number | 1 |

DOIs | |

State | Published - Dec 1 1984 |

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### All Science Journal Classification (ASJC) codes

- Applied Mathematics

### Cite this

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*Annali di Matematica Pura ed Applicata*, vol. 137, no. 1, pp. 163-173. https://doi.org/10.1007/BF01789393

**High order approximation of implicitly defined maps.** / Bressan, Alberto.

Research output: Contribution to journal › Article

TY - JOUR

T1 - High order approximation of implicitly defined maps

AU - Bressan, Alberto

PY - 1984/12/1

Y1 - 1984/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0242673199&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0242673199&partnerID=8YFLogxK

U2 - 10.1007/BF01789393

DO - 10.1007/BF01789393

M3 - Article

AN - SCOPUS:0242673199

VL - 137

SP - 163

EP - 173

JO - Annali di Matematica Pura ed Applicata

JF - Annali di Matematica Pura ed Applicata

SN - 0373-3114

IS - 1

ER -