On geometric and differentiation index of nonlinear differential-algebraic equations

Yahao Chen*, Stephan Trenn*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

2 Citations (Scopus)
12 Downloads (Pure)

Abstract

We discuss two notions of index, i.e., the geometric index and the differentiation index f<j)r nonlinear differential-algebraic equations (DAEs). First, we analyze solutions of nonlinear DAEs by revising a geometric reduction method (see e.g. Rabier and Rheinboldt (2002),Riaza (2008)). Then we show that although both of the geometric index and the differentiation index serve as a measure of difficulties for solving DAEs, they are actually related to the existence and uniqueness of solutions in a different manner. It is claimed in (Campbell and Gear, 1995) that the two indices coincide when sufficient smoothness and assumptions are satisfied, we elaborate this claim and show that the two indices indeed coincide if and only if a condition of uniqueness of solutions is satisfied (under certain constant rank assumptions). Finally, an example of a pendulum system is used to illustrate our results on the two indices.

Original languageEnglish
Title of host publication24th International Symposium on Mathematical Theory of Networks and Systems MTNS 2020
EditorsRodolphe Sepulchre
PublisherElsevier
Pages186-191
Number of pages6
DOIs
Publication statusPublished - 1-Jun-2021
Event24th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2020 - Cambridge, United Kingdom
Duration: 23-Aug-202127-Aug-2021

Publication series

NameIFAC-PapersOnLine
PublisherElsevier
Number9
Volume54
ISSN (Print)2405-8963

Conference

Conference24th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2020
Country/TerritoryUnited Kingdom
CityCambridge
Period23/08/202127/08/2021

Keywords

  • Differential-algebraic equations
  • Differentiation index
  • Existence and uniqueness of solutions
  • Geometric index
  • Geometric method

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