Abstract
This paper deals with two stability aspects of linear systems of the form \({I\ddot{x}+B\dot{x}+Cx=0}\) 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, B 1, C 1) with a symmetrizable matrix C 1. This procedure facilitates stability investigations. We also consider systems with a Hamiltonian spectrum which discloses marginal stability after a Jordan form preserving transformation.
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Stoustrup, J., Pommer, C. & Kliem, W. Stability of linear systems in second-order form based on structure preserving similarity transformations. Z. Angew. Math. Phys. 66, 2909–2919 (2015). https://doi.org/10.1007/s00033-015-0548-4
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DOI: https://doi.org/10.1007/s00033-015-0548-4