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Existence of Metzler Matrices with Given Spectra of Positive Stable Linear Systems and Electrical Circuits

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Abstract

The problem of existence of Metzler matrices with given spectra is addressed for positive stable continuous-time linear systems and electrical circuits. Necessary and sufficient conditions for the existence of the Metzler matrices are established. It is shown that positive and stable electrical circuits have real eigenvalues. An open problem for positive electrical circuits is formulated. The considerations are illustrated by numerical examples of linear systems and positive electrical circuits.

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Acknowledgment

This work was supported by National Science Centre in Poland under work No. 2014/13/B/ST7/03467.

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Authors and Affiliations

  1. Faculty of Electrical Engineering, Białystok University of Technology, Wiejska 45D, 15-351, Białystok, Poland

    Tadeusz Kaczorek

Authors
  1. Tadeusz Kaczorek
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Correspondence to Tadeusz Kaczorek .

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Editors and Affiliations

  1. Automation and Measurements PIAP, Industrial Research Institute for, Warsaw, Poland

    Roman Szewczyk

  2. Automation and Measurements PIAP, Industrial Research Institute for, Warsaw, Poland

    Cezary Zieliński

  3. Automation and Measurements PIAP, Industrial Research Institute for, Warsaw, Poland

    Małgorzata Kaliczyńska

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Kaczorek, T. (2016). Existence of Metzler Matrices with Given Spectra of Positive Stable Linear Systems and Electrical Circuits. In: Szewczyk, R., Zieliński, C., Kaliczyńska, M. (eds) Challenges in Automation, Robotics and Measurement Techniques. ICA 2016. Advances in Intelligent Systems and Computing, vol 440. Springer, Cham. https://doi.org/10.1007/978-3-319-29357-8_13

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  • DOI: https://doi.org/10.1007/978-3-319-29357-8_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-29356-1

  • Online ISBN: 978-3-319-29357-8

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