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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access October 9, 2014

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

  • Maria Adam and Nicholas Assimakis EMAIL logo
From the journal Open Mathematics

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.

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Received: 2013-8-24
Accepted: 2014-7-29
Published Online: 2014-10-9
Published in Print: 2015-1-1

© 2015 Maria Adam, Nicholas Assimakis

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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