Stability of linear systems in second-order form based on structure preserving similarity transformations

Journal Article · Sat Oct 31 00:00:00 EDT 2015 · Zeitschrift fuer Angewandte Mathematik und Physik

DOI:https://doi.org/10.1007/s00033-015-0548-4· OSTI ID:1233775

Stoustrup, Jakob; Pommer, Christian; Kliem, Wolfhard

This paper deals with two stability aspects of linear systems of the form I ¨ x +B˙ x +Cx = 0 given by the triple (I;B;C). A general transformation scheme is given for a structure and Jordan form preserving transformation of the triple. We investigate how a system can be transformed by suitable choices of the transformation parameters into a new system (I;B1;C1) with a symmetrizable matrix C1. This procedure facilitates stability investigations. We also consider systems with a Hamiltonian spectrum which discloses marginal stability after a Jordan form preserving transformation.

• Research Organization: Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
• Sponsoring Organization: USDOE
• DOE Contract Number: AC05-76RL01830
• OSTI ID: 1233775
• Report Number(s): PNNL-SA-105757
• Journal Information: Zeitschrift fuer Angewandte Mathematik und Physik, Vol. 66, Issue 5; ISSN 0044-2275
• Country of Publication: United States
• Language: English