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Positive Linear Control Systems

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Automatic Control, Robotics, and Information Processing

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 296))

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Abstract

This chapter is devoted to the analysis of the positive dynamical linear continuous-time and discrete-time systems. The basic definitions and theorems concerning positivity and stability of the standard and descriptor (singular) linear systems described by the state equation and transfer matrices are given. The Kharitonov theorem is extended to positive linear systems with interval state matrices. The notions of the convex combinations of Hurwitz polynomials and Schur polynomials and of the state matrices are introduced. The considerations are illustrated by numerical examples of positive linear continuous-time and discrete-time systems.

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Acknowledgements

This work was supported by National Science Centre in Poland under work No. 2017/27/B/ST7/02443.

I wish to thank very much to Dr. Łukasz Sajewski and Dr. Kamil Borawski for their essential help in preparation of the finale version of this chapter.

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Authors and Affiliations

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

    Tadeusz Kaczorek

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  1. Tadeusz Kaczorek
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Correspondence to Tadeusz Kaczorek .

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Editors and Affiliations

  1. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Piotr Kulczycki

  2. Institute of Control and Computation Engineering, University of Zielona Góra, Zielona Góra, Poland

    Józef Korbicz

  3. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Janusz Kacprzyk

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Kaczorek, T. (2021). Positive Linear Control Systems. In: Kulczycki, P., Korbicz, J., Kacprzyk, J. (eds) Automatic Control, Robotics, and Information Processing. Studies in Systems, Decision and Control, vol 296. Springer, Cham. https://doi.org/10.1007/978-3-030-48587-0_8

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