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Distributed solving Sylvester equations with fractional order dynamics

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Abstract

This paper addresses distributed computation Sylvester equations of the form \({A}{X}+{X}{B}={C}\) with fractional order dynamics. By partitioning parameter matrices A, B and C, we transfer the problem of distributed solving Sylvester equations as two distributed optimization models and design two fractional order continuous-time algorithms, which have more design freedom and have potential to obtain better convergence performance than that of existing first order algorithms. Then, rewriting distributed algorithms as corresponding frequency distributed models, we design Lyapunov functions and prove that proposed algorithms asymptotically converge to an exact or least squares solution. Finally, we validate the effectiveness of proposed algorithms by providing a numerical example

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China (nos. 61903027, 61973002), and in part by the National Postdoctoral Program for Innovative Talents (BX20180346), and in part by the General Financial Grant from the China Postdoctoral Science Foundation (2019M660834), and in part by the Anhui Provincial Natural Science Foundation (no. 2008085J32).

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Authors and Affiliations

  1. Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, School of Electrical Engineering and Automation, Anhui University, Hefei, 230601, Anhui, China

    Songsong Cheng & Yuan Fan

  2. Key Laboratory of Knowledge Automation for Industrial Processes of Ministry of Education, School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing, 100083, China

    Shu Liang

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  1. Songsong Cheng
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  2. Shu Liang
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  3. Yuan Fan
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Correspondence to Yuan Fan.

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Cheng, S., Liang, S. & Fan, Y. Distributed solving Sylvester equations with fractional order dynamics. Control Theory Technol. 19, 249–259 (2021). https://doi.org/10.1007/s11768-021-00044-0

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