Fast iterative solutions of Riccati and Lyapunov equations-Reference-Cited by-同舟云学术

Fast iterative solutions of Riccati and Lyapunov equations

Published:2022-01-01 Issue:1 Volume:20 Page:1845-1857
ISSN:2391-5455
Container-title:Open Mathematics
language:en
Short-container-title:

Author:

Assimakis Nicholas¹,Adam Maria²

Affiliation:

1. Department of Digital Industry Technologies, National and Kapodistrian University of Athens , Psachna Evias , Greece

2. Department of Computer Science and Biomedical Informatics, University of Thessaly , Lamia , Greece

Abstract

AbstractIn this article, new iterative algorithms for solving the discrete Riccati and Lyapunov equations are derived in the case where the transition matrix is diagonalizable with real eigenvalues. It is shown that the proposed iterative algorithms are faster than the classical ones, even for a small number of iterations.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/math-2022-0546/pdf

Reference20 articles.

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3. D. S. Bernstein, Matrix Mathematics: Theory Facts and Formulas with Application to Linear Systems Theory, Princeton University Press, Princeton, NJ, 2005.

4. C. Kojima, K. Takaba, O. Kaneko, and P. Rapisarda, A characterization of solutions of the discrete-time algebraic riccati equation based on quadratic difference forms, Linear Algebra Appl. 416 (2006), 1060–1082.

5. A. Nakhmani, Modern Control: State-Space Analysis and Design Methods, McGraw Hill, New York, 2020.

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