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Conference on Automation

AUTOMATION 2019: Automation 2019 pp 245–257Cite as

Digraphs Structures with Weights Corresponding to One-Dimensional Fractional Systems

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 920))

Abstract

In this paper, after extensive study and experimentation, the first classification of digraphs structures \(\mathcal {D}\) corresponding to one-dimensional (1D) fractional continuous-time and discrete-time systems has been presented. It was found that digraph structures created can be divided into three classes \(\mathcal {K}_1\), \(\mathcal {K}_2\), \(\mathcal {K}_3\) with a different feasibility for different polynomials. Additional two cases of possible input-output digraph structure \(\mathcal {IO}_{1}\), \(\mathcal {IO}_{2}\) was investigated and discussed. It should be noted, that the proposed digraph classes give the opportunity to easily determine the realization of the dynamic system as a set of matrices \((\mathbf {A},\mathbf {B},\mathbf {C})\). The proposed digraphs classification was illustrated with some numerical examples.

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Authors and Affiliations

  1. Faculty of Electrical Engineering, Institute of Control and Industrial Electronics, Warsaw University of Technology, Koszykowa 75, 00-662, Warsaw, Poland

    Konrad Andrzej Markowski

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  1. Konrad Andrzej Markowski
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Correspondence to Konrad Andrzej Markowski .

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Editors and Affiliations

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

    Roman Szewczyk

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

    Cezary Zieliński

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

    Małgorzata Kaliczyńska

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Markowski, K.A. (2020). Digraphs Structures with Weights Corresponding to One-Dimensional Fractional Systems. In: Szewczyk, R., Zieliński, C., Kaliczyńska, M. (eds) Automation 2019. AUTOMATION 2019. Advances in Intelligent Systems and Computing, vol 920. Springer, Cham. https://doi.org/10.1007/978-3-030-13273-6_24

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