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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo

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Open Access
Online
ISSN
2391-5455
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Volume 13, Issue 1 (Jan 2015)

Issues

Nonrecursive solution for the discrete algebraic Riccati equation and X + A*X-1A=L

Maria Adam
  • Department of Computer Science and Biomedical Informatics, University of Thessaly, 2-4 Papasiopoulou str., P.O. 35100 Lamia, Greece
  • Email:
/ Nicholas Assimakis
  • Corresponding author
  • Department of Electronic Engineering, Technological Educational Institute of Central Greece, 3rd km Old National Road Lamia-Athens, P.O. 35100 Lamia, Greece
  • Email:
Published Online: 2014-10-09 | DOI: https://doi.org/10.1515/math-2015-0006

Abstract

In this paper, we present two new algebraic algorithms for the solution of the discrete algebraic Riccati equation. The first algorithm requires the nonsingularity of the transition matrix and is based on the solution of a standard eigenvalue problem for a new symplectic matrix; the proposed algorithm computes the extreme solutions of the discrete algebraic Riccati equation. The second algorithm solves the Riccati equation without the assumption of the nonsingularity of the transition matrix; the proposed algorithm is based on the solution of the matrix equation X + A*X-1A=L, where A is a singular matrix and L a positive definite matrix.

Keywords : Discrete algebraic Riccati equation; Nonlinear matrix equation; Positive definite solution; Stability

References

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About the article

Received: 2013-08-24

Accepted: 2014-07-29

Published Online: 2014-10-09

Published in Print: 2015-01-01


Citation Information: Open Mathematics, ISSN (Online) 2391-5455, DOI: https://doi.org/10.1515/math-2015-0006. Export Citation

© 2015 Maria Adam, Nicholas Assimakis. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. (CC BY-NC-ND 3.0)

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