A linear relation approach to port-hamiltonian differential-algebraic equations

Publikationstyp
Journal Article
Date Issued
2021
Sprache
English
Author(s)
Gernandt, Hannes  
Haller, Frédéric  
Reis, Timo  
Institut
Mechanik und Meerestechnik M-13  
TORE-URI
http://hdl.handle.net/11420/10740
Journal
SIAM journal on matrix analysis and applications  
Volume
42
Issue
2
Start Page
1011
End Page
1044
Citation
SIAM Journal on Matrix Analysis and Applications 42 (2): 1011-1044 (2021)
Publisher DOI
10.1137/20M1371166
Scopus ID
2-s2.0-85107650473
Publisher
Soc.
We consider linear port-Hamiltonian differential-algebraic equations. Inspired by the geometric approach of van der Schaft and Maschke [System Control Lett., 121 (2018), pp. 31-37] and the linear algebraic approach of Mehl, Mehrmann, and Wojtylak [SIAM J. Matrix Anal. Appl., 39 (2018), pp. 1489-1519], we present another view by using the theory of linear relations. We show that this allows us to elaborate the differences and mutualities of the geometric and linear algebraic views, and we introduce a class of DAEs which comprises these two approaches. We further study the properties of matrix pencils arising from our approach via linear relations.
Subjects
differential-algebraic equations
Linear relations
Matrix pencils
Port-Hamiltonian systems
DDC Class
510: Mathematik
600: Technik