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Journal of Computational and Applied Mathematics, ISSN 0377-0427, 03/2015, Volume 277, pp. 115 - 126
We consider the numerical solution of large-scale discrete-time algebraic Riccati equations. The doubling algorithm is adapted, with the iterates for A not... 
Large-scale problem | Doubling algorithm | Discrete-time algebraic Riccati equation | Discrete-time algebraic | Riccati equation | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | LYAPUNOV EQUATIONS | RECIPES | KRYLOV SUBSPACE METHODS | Analysis | Algorithms
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 04/2019, Volume 350, pp. 80 - 86
A fast iterative algorithm is proposed for numerically computing an interval matrix containing the Hermitian positive definite solution to the conjugate... 
Hermitian positive definite solution | Verified numerical computation | Perron–Frobenius theory | Discrete-time algebraic Riccati equation | MATHEMATICS, APPLIED | Perron-Frobenius theory | Algorithms
Journal Article
Automatica, ISSN 0005-1098, 09/2017, Volume 83, pp. 47 - 57
Journal Article
Japan Journal of Industrial and Applied Mathematics, ISSN 0916-7005, 9/2019, Volume 36, Issue 3, pp. 763 - 776
A robust algorithm is proposed for numerically computing an interval matrix containing the stabilizing solution of a discrete-time algebraic Riccati equation.... 
Computational Mathematics and Numerical Analysis | 39B42 | 15A24 | 65G20 | Verified numerical computation | Perron–Frobenius theory | Mathematics | Applications of Mathematics | Stabilizing solution | Discrete-time algebraic Riccati equation | VERIFIED COMPUTATION | MATHEMATICS, APPLIED | Perron-Frobenius theory
Journal Article
Asian Journal of Control, ISSN 1561-8625, 01/2013, Volume 15, Issue 1, pp. 132 - 141
In the present paper we obtain an explicit closed‐form solution for the discrete‐time algebraic Riccati equation (DTARE) with vanishing state weight, whenever... 
optimal control | Discrete‐time algebraic Riccati equation | linear systems | Discrete-time algebraic Riccati equation | NETWORKED CONTROL-SYSTEMS | FEEDBACK STABILIZATION | CLOSED-FORM SOLUTION | CHANNELS | AUTOMATION & CONTROL SYSTEMS
Journal Article
Operators and Matrices, ISSN 1846-3886, 03/2018, Volume 12, Issue 1, pp. 169 - 187
The purpose of this paper is to introduce a two-stage procedure that can be used to decompose a discrete-time algebraic Riccati equation into a trivial part, a... 
Symplectic pencil | Discrete-time algebraic Riccati equations | MATHEMATICS | ORDER REDUCTION | FILTERS | symplectic pencil | CLOSED-LOOP MATRIX | SYSTEMS | CONVERGENCE | TIME | STOCHASTIC-CONTROL
Journal Article
IEEE Transactions on Automatic Control, ISSN 0018-9286, 03/2019, Volume 64, Issue 3, pp. 1125 - 1136
Journal Article
Discrete Dynamics in Nature and Society, ISSN 1026-0226, 2015, Volume 2015, pp. 1 - 11
We provide necessary and sufficient conditions for the existence of stabilizing solutions for a class of modified algebraic discrete-time Riccati equations... 
LINEAR-SYSTEMS | HILBERT-SPACES | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | OPERATORS | MULTIDISCIPLINARY SCIENCES | ORDERED BANACH-SPACES | Discrete-time systems | Research | Riccati equation | Mathematical research | Linear systems | Operators | Algebra | Mathematical analysis | Markov processes | Banach space | Linear quadratic
Journal Article
Applied Numerical Mathematics, ISSN 0168-9274, 06/2020, Volume 152, pp. 499 - 510
We apply the Krylov subspace methods to large-scale discrete-time algebraic Riccati equations. The solvability of the projected algebraic Riccati equation is... 
Inheritance property | Krylov subspace | LQR optimal control | Projection methods | Discrete-time algebraic Riccati equation
Journal Article
SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, 2009, Volume 31, Issue 3, pp. 1257 - 1278
A discrete-time nonsymmetric algebraic Riccati system which incorporates as special cases of various discrete-time nonsymmetric algebraic Riccati equations is... 
Discrete-time nonsymmetric algebraic riccati equations | Matrix pencil | Deflating subspaces | Game theory | IMPROVED ALGORITHM | MATHEMATICS, APPLIED | discrete-time nonsymmetric algebraic Riccati equations | game theory | matrix pencil | PARAMETRIZATION | COMPUTATION | deflating subspaces | Studies | Matrix | Engineering Sciences | Automatic
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 2008, Volume 206, Issue 1, pp. 34 - 41
We consider a set of discrete-time coupled algebraic Riccati equations that arise in quadratic optimal control. Two iterations for computing a symmetric... 
Stein equation | Positive definite solution | Jump systems | A set of discrete-time Riccati equations | MATHEMATICS, APPLIED | JUMP LINEAR-SYSTEMS | LYAPUNOV ITERATIONS | Analysis | Methods | Algorithms
Journal Article
Automatica, ISSN 0005-1098, 01/2018, Volume 87, pp. 383 - 388
Journal Article
International Journal of Robust and Nonlinear Control, ISSN 1049-8923, 11/2017, Volume 27, Issue 16, pp. 2921 - 2936
Journal Article
IEEE Transactions on Signal Processing, ISSN 1053-587X, 05/2015, Volume 63, Issue 10, pp. 2559 - 2571
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 2006, Volume 416, Issue 2, pp. 1060 - 1082
Journal Article
IEEE Transactions on Automatic Control, ISSN 0018-9286, 07/2017, Volume 62, Issue 7, pp. 3262 - 3276
Journal Article
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