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

Maria Adam; Nicholas Assimakis

Open Mathematics (2015)

  • Volume: 13, Issue: 1, page 51-63, electronic only
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Maria Adam, and Nicholas Assimakis. " Nonrecursive solution for the discrete algebraic Riccati equation and X + A*X -1 A=L ." Open Mathematics 13.1 (2015): 51-63, electronic only. <http://eudml.org/doc/268822>.

@article{MariaAdam2015,
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.},
author = {Maria Adam, Nicholas Assimakis},
journal = {Open Mathematics},
keywords = {Discrete algebraic Riccati equation; Nonlinear matrix equation; Positive definite solution; Stability; discrete algebraic Riccati equation; nonlinear matrix equation; positive definite solution; stability; algorithm},
language = {eng},
number = {1},
pages = {51-63, electronic only},
title = { Nonrecursive solution for the discrete algebraic Riccati equation and X + A*X -1 A=L },
url = {http://eudml.org/doc/268822},
volume = {13},
year = {2015},
}

TY - JOUR
AU - Maria Adam
AU - Nicholas Assimakis
TI - Nonrecursive solution for the discrete algebraic Riccati equation and X + A*X -1 A=L
JO - Open Mathematics
PY - 2015
VL - 13
IS - 1
SP - 51
EP - 63, electronic only
AB - 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.
LA - eng
KW - Discrete algebraic Riccati equation; Nonlinear matrix equation; Positive definite solution; Stability; discrete algebraic Riccati equation; nonlinear matrix equation; positive definite solution; stability; algorithm
UR - http://eudml.org/doc/268822
ER -

References

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