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Newton’s method for the positive solution of the coupled algebraic Riccati equation applied to automatic control

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Abstract

In this paper, we discuss the existence of the positive solution for the coupled algebraic Riccati equation which is usually encountered in control theory. When this equation has a positive solution, Newton’s method is presented to find the minimal positive solution. Furthermore, we show some properties of Newton’s iteration method. Finally, we give corresponding numerical examples to demonstrate the effectiveness of the derived iteration method.

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Author information

Author notes

  1. Jianzhou Liu and Juan Zhang have contributed equally to this work and should be considered as co-first authors.

Authors and Affiliations

  1. Department of Mathematics and Computational Science, Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan, 411105, Hunan, People’s Republic of China

    Jianzhou Liu, Juan Zhang & Fangfang Luo

Authors
  1. Jianzhou Liu
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  2. Juan Zhang
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  3. Fangfang Luo
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Corresponding authors

Correspondence to Jianzhou Liu or Juan Zhang.

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Communicated by Enrique Zuazua.

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The work was supported in part by National Natural Science Foundation of China (11971413, 11771368, 11771370), Natural Science Foundation of Hunan Province (2018JJ2376, 2017JJ3305), and Project of Education Department of Hunan Province (18B057, 19A500).

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Liu, J., Zhang, J. & Luo, F. Newton’s method for the positive solution of the coupled algebraic Riccati equation applied to automatic control. Comp. Appl. Math. 39, 113 (2020). https://doi.org/10.1007/s40314-020-01143-5

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  • DOI: https://doi.org/10.1007/s40314-020-01143-5

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