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Nonsingularity of Grain-like cascade FSRs via semi-tensor product

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  • Special Focus on Analysis and Control of Finite-Valued Network Systems
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Abstract

In this paper, Grain-like cascade feedback shift registers (FSRs) are regarded as two Boolean networks (BNs), and the semi-tensor product (STP) of the matrices is used to convert the Grain-like cascade FSRs into an equivalent linear equation. Based on the STP, a novel method is proposed herein to investigate the nonsingularity of Grain-like cascade FSRs. First, we investigate the property of the state transition matrix of Grain-like cascade FSRs. We then propose their sufficient and necessary nonsingularity condition. Next, we regard the Grain-like cascade FSRs as Boolean control networks (BCNs) and further provide a sufficient condition of their nonsingularity. Finally, two examples are provided to illustrate the results obtained in this paper.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 61573102, 11671361), Natural Science Foundation of Jiangsu Province of China (Grant No. BK20170019), Jiangsu Provincial Key Laboratory of Networked Collective Intelligence (Grant No. BM2017002), China Postdoctoral Science Foundation (Grant Nos. 2014M560377, 2015T80483), Jiangsu Province Six Talent Peaks Project (Grant No. 2015-ZNDW-002), and Fundamental Research Funds for the Central Universities.

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Authors and Affiliations

  1. School of Mathematics, Southeast University, Nanjing, 210096, China

    Jianquan Lu & Meilin Li

  2. College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua, 321004, China

    Jianquan Lu & Yang Liu

  3. Department of Mathematics, Hong Kong, China

    Daniel W.C. Ho

  4. Potsdam Institute for Climate Impact Research, Potsdam, 14415, Germany

    Jürgen. Kurths

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  1. Jianquan Lu
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  2. Meilin Li
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Correspondence to Jianquan Lu.

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Lu, J., Li, M., Liu, Y. et al. Nonsingularity of Grain-like cascade FSRs via semi-tensor product. Sci. China Inf. Sci. 61, 010204 (2018). https://doi.org/10.1007/s11432-017-9269-6

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