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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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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