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Pseudospectra of Loewner Matrix Pencils

In: Realization and Model Reduction of Dynamical Systems

Author

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  • Mark Embree

    (Academy of Integrated Science, Virginia Tech, Department of Mathematics and Computational Modeling and Data Analytics Division)

  • A. Cosmin Ioniţă

    (The MathWorks Inc.)

Abstract

Loewner matrix pencils play a central role in the system realization theory of Mayo and Antoulas, an important development in data-driven modeling. The eigenvalues of these pencils reveal system poles. How robust are the poles recovered via Loewner realization? With several simple examples, we show how pseudospectra of Loewner pencils can be used to investigate the influence of interpolation point location and partitioning on pole stability, the transient behavior of the realized system, and the effect of noisy measurement data. We include an algorithm to efficiently compute such pseudospectra by exploiting Loewner structure.

Suggested Citation

  • Mark Embree & A. Cosmin Ioniţă, 2022. "Pseudospectra of Loewner Matrix Pencils," Springer Books, in: Christopher Beattie & Peter Benner & Mark Embree & Serkan Gugercin & Sanda Lefteriu (ed.), Realization and Model Reduction of Dynamical Systems, pages 59-78, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-95157-3_4
    DOI: 10.1007/978-3-030-95157-3_4
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