October 31, 2015
Journal Article

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

Abstract

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.

Revised: January 5, 2016 | Published: October 31, 2015

Citation

Stoustrup J., C. Pommer, and W. Kliem. 2015. Stability of linear systems in second-order form based on structure preserving similarity transformations. Zeitschrift für Angewandte Mathematik und Physik 66, no. 5:2909-2919. PNNL-SA-105757. doi:10.1007/s00033-015-0548-4