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Iterative algorithms with the latest update for Riccati matrix equations in Itô Markov jump systems

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Abstract

This study is concerned with the problem to solve the continuous coupled Riccati matrix equations in Itô Markov jump systems. A new iterative algorithm is developed by using the latest estimation information and introducing a tuning parameter. The iterative solution obtained by the proposed algorithm with zero initial conditions converges to the unique positive definite solution of the considered equations. The convergence rate of the algorithm is dependent on the adjustable parameter. Furthermore, a numerical example is provided to show the effectiveness of the presented algorithms.

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Author notes

  1. These authors contributed equally to this work.

Authors and Affiliations

  1. School of Mechanical Engineering and Automation, Harbin Institute of Technology, Shenzhen, 518055, China

    Chuang Ma, Zhi Li, WanQi Wu & Ying Zhang

Authors
  1. Chuang Ma
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  2. Zhi Li
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  3. WanQi Wu
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  4. Ying Zhang
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Corresponding authors

Correspondence to Chuang Ma or Zhi Li.

Additional information

This work was supported by the Shenzhen Municipal Basic Research Project for Discipline Layout (Grant No. JCYJ20170811160715620), the National Natural Science Foundation of China for Excellent Young Scholars (Grant No. 61822305), the Shenzhen Municipal Project for International Cooperation (Grant No. GJHZ20180420180849805), and the Guangdong Natural Science Foundation (Grant No. 2017A030313340).

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Ma, C., Li, Z., Wu, W. et al. Iterative algorithms with the latest update for Riccati matrix equations in Itô Markov jump systems. Sci. China Technol. Sci. 63, 1577–1584 (2020). https://doi.org/10.1007/s11431-020-1668-4

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  • DOI: https://doi.org/10.1007/s11431-020-1668-4

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