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On the Stabilizability for a Class of Linear Time-Invariant Systems Under Uncertainty

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Abstract

The uncertainty principle is one of the most important features in modeling and solving linear time-invariant (LTI) systems. The neutrality phenomena of some factors in real models have been widely recognized by engineers and scientists. The convenience and flexibility of neutrosophic theory in the description and differentiation of uncertainty terms make it take advantage of modeling and designing of control systems. This paper deals with the controllability and stabilizability of LTI systems containing neutrosophic uncertainty in the sense of both indeterminacy parameters and functional relationships. We define some properties and operators between neutrosophic numbers via horizontal membership function of a relative-distance-measure variable. Results on exponential matrices of neutrosophic numbers are well-defined with the notion \(e^{tA}\) deployed in a series of neutrosophic matrices. Moreover, we introduce the concepts of controllability and stabilizability of neutrosophic systems in the sense of Granular derivatives. Sufficient conditions to guarantee the controllability of neutrosophic LTI systems are established. Some numerical examples, related to RLC circuit and DC motor systems, are exhibited to illustrate the effectiveness of theoretical results.

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Acknowledgements

The authors are greatly indebted to Editor-in-Chief, Associate Editor, and the anonymous referees for their helpful comments and valuable suggestions, that greatly improve the quality and clarity of the paper. This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No. 101.02-2018.311.

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Authors and Affiliations

  1. Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Nguyen Thi Kim Son

  2. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Nguyen Thi Kim Son

  3. Department of Mathematics, Hanoi Pedagogical University 2, Phuc Yen City, Vietnam

    Nguyen Phuong Dong

  4. VNU Information Technology Institute, Vietnam National University, Hanoi, Vietnam

    Le Hoang Son

  5. Department of Operations Research and Decision Support, Faculty of Computers and Informatics, Zagazig University, Zagazig, Egypt

    Mohamed Abdel-Basset

  6. University of California, Davis, USA

    Gunasekaran Manogaran

  7. Faculty of Information Technology, People’s Police University of Technology and Logistics, Bac Ninh, Viet Nam

    Hoang Viet Long

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  1. Nguyen Thi Kim Son
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Son, N.T.K., Dong, N.P., Son, L.H. et al. On the Stabilizability for a Class of Linear Time-Invariant Systems Under Uncertainty. Circuits Syst Signal Process 39, 919–960 (2020). https://doi.org/10.1007/s00034-019-01248-1

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  • DOI: https://doi.org/10.1007/s00034-019-01248-1

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