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Robust verification algorithm for stabilizing solutions of discrete-time algebraic Riccati equations

  • Shinya MiyajimaEmail author
Original Paper
  • 15 Downloads

Abstract

A robust algorithm is proposed for numerically computing an interval matrix containing the stabilizing solution of a discrete-time algebraic Riccati equation. This algorithm is based on estimating an upper bound for the spectral radius of a matrix power utilizing the Perron–Frobenius theory. The algorithm moreover verifies the uniqueness of the contained solution. Numerical results show that the algorithm is more successful than the previous algorithms.

Keywords

Discrete-time algebraic Riccati equation Stabilizing solution Verified numerical computation Perron–Frobenius theory 

Mathematics Subject Classification

15A24 39B42 65G20 

Notes

Acknowledgements

The author acknowledges the reviewer for valuable comments.

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Copyright information

© The JJIAM Publishing Committee and Springer Japan KK, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Faculty of Science and EngineeringIwate UniversityMorioka-shiJapan

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