TY - JOUR
T1 - Riesz Bases Of Port-Hamiltonian Systems
AU - Jacob, Birgit
AU - Kaiser, Julia T.
AU - Zwart, Hans
N1 - Funding Information:
\ast Received by the editors September 14, 2020; accepted for publication (in revised form) August 11, 2021; published electronically December 16, 2021. https://doi.org/10.1137/20M1366216 Funding: This work was funded by Deutsche Forschungsgemeinschaft grant JA 735/13-1. \dagger IMACM, School of Mathematics and Natural Sciences, University of Wuppertal, D-42119 Wuppertal, Germany ([email protected], [email protected]). \ddagger Department of Applied Mathematics, University of Twente, 7500 AE Enschede, The Netherlands, and Department of Mechanical Engineering, Technische Universiteit Eindhoven, 5600 MB Eindhoven, The Netherlands ([email protected]).
Publisher Copyright:
© 2021 Society for Industrial and Applied Mathematics Publications. All rights reserved.
PY - 2021
Y1 - 2021
N2 - The location of the spectrum and the Riesz basis property of well-posed homogeneous infinite-dimensional linear port-Hamiltonian systems on a one-dimensional spatial domain are studied. It is shown that the Riesz basis property is equivalent to the fact that the system operator generates a strongly continuous group. Moreover, in this situation the spectrum consists of eigenvalues only, located in a strip parallel to the imaginary axis and they can decomposed into finitely many sets each having a uniform gap.
AB - The location of the spectrum and the Riesz basis property of well-posed homogeneous infinite-dimensional linear port-Hamiltonian systems on a one-dimensional spatial domain are studied. It is shown that the Riesz basis property is equivalent to the fact that the system operator generates a strongly continuous group. Moreover, in this situation the spectrum consists of eigenvalues only, located in a strip parallel to the imaginary axis and they can decomposed into finitely many sets each having a uniform gap.
KW - infinite-dimensional linear port-Hamiltonian system
KW - Riesz spectral operator
KW - strongly continuous group
UR - http://www.scopus.com/inward/record.url?scp=85124640795&partnerID=8YFLogxK
U2 - 10.1137/20M1366216
DO - 10.1137/20M1366216
M3 - Article
AN - SCOPUS:85124640795
SN - 0363-0129
VL - 59
SP - 4646
EP - 4665
JO - SIAM journal on control and optimization
JF - SIAM journal on control and optimization
IS - 6
ER -