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

Stoustrup, Jakob; Pommer, Christian; Kliem, Wolfhard

doi:10.1007/s00033-015-0548-4

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

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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.

Authors:: Stoustrup, Jakob; Pommer, Christian; Kliem, Wolfhard

Publication Date:: Sat Oct 31 00:00:00 EDT 2015

Research Org.:: Pacific Northwest National Lab. (PNNL), Richland, WA (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1233775

Report Number(s):: PNNL-SA-105757
Journal ID: ISSN 0044-2275

DOE Contract Number:: AC05-76RL01830

Resource Type:: Journal Article

Journal Name:: Zeitschrift fuer Angewandte Mathematik und Physik

Additional Journal Information:: Journal Volume: 66; Journal Issue: 5; Journal ID: ISSN 0044-2275

Country of Publication:: United States

Language:: English

Citation Formats


                    Stoustrup, Jakob, Pommer, Christian, and Kliem, Wolfhard. Stability of linear systems in second-order form based on structure preserving similarity transformations.  United States: N. p., 2015. 
        Web.  doi:10.1007/s00033-015-0548-4.

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                    Stoustrup, Jakob, Pommer, Christian, & Kliem, Wolfhard. Stability of linear systems in second-order form based on structure preserving similarity transformations.  United States.  https://doi.org/10.1007/s00033-015-0548-4

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                    Stoustrup, Jakob, Pommer, Christian, and Kliem, Wolfhard. 2015.  
        "Stability of linear systems in second-order form based on structure preserving similarity transformations".  United States.  https://doi.org/10.1007/s00033-015-0548-4.

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@article{osti_1233775,

  title        = {Stability of linear systems in second-order form based on structure preserving similarity transformations},

  author       = {Stoustrup, Jakob and Pommer, Christian and Kliem, Wolfhard},

  abstractNote = {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.},

  doi          = {10.1007/s00033-015-0548-4},

  url          = {https://www.osti.gov/biblio/1233775},
  journal      = {Zeitschrift fuer Angewandte Mathematik und Physik},

  issn         = {0044-2275},

  number       = 5,

  volume       = 66,

  place        = {United States},

  year         = {Sat Oct 31 00:00:00 EDT 2015},

  month        = {Sat Oct 31 00:00:00 EDT 2015}

}

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