Abstract
This paper introduces the first classification of digraph structures corresponding to characteristic polynomials. It was found that digraph structures created can be divided into three classes with different feasibility for different polynomials—only structures of one class are found to be independent from wages of polynomial’s terms. In this paper classification of structures is described, along with method how to divide them and illustrated with examples.
Research has been financed with the funds of the Statutory Research of 2016.
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References
Bang-Jensen, J., Gutin, G.: Digraphs: Theory, Algorithms and Applications, 2nd edn. Springer, London (2009)
Blyth, T., Robertson, E.: Basic Linear Algebra, 2nd edn. Springer, London (2002)
Fornasini, E., Valcher, M.E.: Directed graphs, 2D state models, and characteristic polynomials of irreducible matrix pairs. Linear Algebra Appl. 263, 275–310 (1997)
Fornasini, E., Valcher, M.E.: On the positive reachability of 2D positive systems. LCNIS 297–304 (2003)
Hryniów, K., Markowski, K.A.: Parallel digraphs-building algorithm for polynomial realisations. In: Proceedings of 2014 15th International Carpathian Control Conference (ICCC), pp. 174–179 (2014). http://dx.doi.org/10.1109/CarpathianCC.2014.6843592
Hryniów, K., Markowski, K.A.: Digraphs minimal realisations of state matrices for fractional positive systems. In: R. Szewczyk, C. Zieliński, M. Kaliczyńska (eds.) Progress in Automation, Robotics and Measuring Techniques, Advances in Intelligent Systems and Computing, vol. 350, pp. 63–72. Springer (2015). doi:10.1007/978-3-319-15796-2_7. http://dx.doi.org/10.1007/978-3-319-15796-2_7
Hryniów, K., Markowski, K.A.: Parallel multi-dimensional digraphs-building algorithm for finding a complete set of positive characteristic polynomial realisations of dynamic system. Appl. Math. Comput. (Submitted to)
Kaczorek, T.: Polynomial and Rational Matrices. Springer, London (2007)
Wallis, W.D.: A Beginner’s Guide to Graph Theory. Biiokhäuser (2007)
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Hryniów, K., Markowski, K.A. (2016). Classes of Digraph Structures Corresponding to Characteristic Polynomials. 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_30
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DOI: https://doi.org/10.1007/978-3-319-29357-8_30
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