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Fast verified computation for solutions of continuous-time algebraic Riccati equations

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Abstract

A fast numerical algorithm for computing interval matrices containing solutions of continuous-time algebraic Riccati equations is proposed. This algorithm utilizes numerical spectral decomposition and involves only cubic complexity. Stabilizing and anti-stabilizing properties and uniqueness of the contained solution can moreover be verified by this algorithm. Numerical results show the property of this algorithm.

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Notes

  1. Even if we exploit numerical spectral decomposition of \(A - B\tilde{X}\) instead, analogous discussion is possible, although description will become more complicated.

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Acknowledgments

The author thanks Dr. Behnam Hashemi and Prof. Siegfried M. Rump of Shiraz University of Technology and Hamburg University of Technology, respectively, for fruitful discussions. The author also acknowledges the referee for the valuable comments.

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Authors and Affiliations

  1. Faculty of Engineering, Gifu University, 1-1 Yanagido, Gifu-shi, Gifu, 501-1193, Japan

    Shinya Miyajima

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  1. Shinya Miyajima
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Correspondence to Shinya Miyajima.

Additional information

This research was partially supported by Grant-in-Aid for Scientific Research (C) (23560066, 2011–2015) from the Ministry of Education, Culture, Sports, Science and Technology of Japan.

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Miyajima, S. Fast verified computation for solutions of continuous-time algebraic Riccati equations. Japan J. Indust. Appl. Math. 32, 529–544 (2015). https://doi.org/10.1007/s13160-015-0178-4

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  • DOI: https://doi.org/10.1007/s13160-015-0178-4

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