The matrix bounds and fixed-point iteration for the solution of the discrete algebraic Riccati equation

2018 ◽  
Vol 36 (02) ◽  
pp. 681-699
Author(s):  
Juan Zhang ◽  
Jianzhou Liu
Keyword(s):  
Fixed Point ◽  
Riccati Equation ◽  
Algebraic Riccati Equation ◽  
Fixed Point Iteration ◽  
The Matrix ◽  
Discrete Algebraic Riccati Equation

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

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Maria Adam ◽  
Nicholas Assimakis
Keyword(s):  
Riccati Equation ◽  
Transition Matrix ◽  
Positive Definite Matrix ◽  
Algebraic Riccati Equation ◽  
Singular Matrix ◽  
Symplectic Matrix ◽  
Algebraic Algorithms ◽  
The Matrix ◽  
Discrete Algebraic Riccati Equation ◽  
Extreme Solutions

AbstractIn 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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