F. A. Aliev and V. B. Larin, Optimization of Linear Control Systems: Analytical Methods and Computational Algorithms, of Stability and Control: Theory, Methods and Applications. Gordon and Breach, 1998.

A. H. Mohy and N. J. Higham, Computing the Fr??chet Derivative of the Matrix Exponential, with an Application to Condition Number Estimation, SIAM Journal on Matrix Analysis and Applications, vol.30, issue.4, pp.1639-1657, 2009.
DOI : 10.1137/080716426

A. H. Mohy and N. J. Higham, The complex step approximation to the Fr??chet derivative of a matrix function, Numerical Algorithms, vol.250, issue.1, pp.133-148, 2010.
DOI : 10.1137/1.9780898718898

A. H. Al-mohy, N. J. Higham, and S. D. Relton, Computing the Fr??chet Derivative of the Matrix Logarithm and Estimating the Condition Number, SIAM Journal on Scientific Computing, vol.35, issue.4, 2013.
DOI : 10.1137/120885991

T. Ando and J. L. Van-hemmen, An inequality for trace ideals, Commun. Math. Phys, vol.76, pp.143-148, 1980.

A. Andrews, A square root formulation of the Kalman covariance equations., AIAA Journal, vol.57, issue.6, pp.1165-1166, 1968.
DOI : 10.2514/3.4189

R. H. Bartels and G. W. Stewart, Solution of the matrix equation AX + XB = C [F4], Communications of the ACM, vol.15, issue.9, pp.820-826, 1972.
DOI : 10.1145/361573.361582

R. Bhatia and M. Uchiyama, The operator equation <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msubsup><mml:mrow><mml:mo>???</mml:mo></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msubsup><mml:msup><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mo>-</mml:mo><mml:mi>i</mml:mi></mml:mrow></mml:msup><mml:msup><mml:mrow><mml:mtext><ce:italic>XB</ce:italic></mml:mtext></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:mi>Y</mml:mi></mml:math>, Expositiones Mathematicae, vol.27, issue.3, pp.251-255, 2009.
DOI : 10.1016/j.exmath.2009.02.001

G. J. Bierman-;-m, . S. Belzer-;-j, and . W. Vandergraft-;-d, Maximum likelihood estimation using square root information filters, IEEE Transactions on Automatic Control, vol.35, issue.12, pp.1293-1298, 1990.
DOI : 10.1109/9.61004

A. N. Bishop, P. Del-moral, and A. Niclas, A perturbation analysis of stochastic matrix Riccati diffusions, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01593830

R. W. Brockett, Finite dimensional linear systems, Society for Industrial and Applied Mathematics, 2015.
DOI : 10.1137/1.9781611973884

J. R. Cardoso, Evaluating the Fréchet derivative of the matrix p-th root, Electronic Transactions on Numerical Analysis, vol.38, pp.202-217, 2011.

R. Bellman, Some inequalities for the square root of a positive definite matrix. Linear Algebra and its applications, pp.321-324, 1968.

S. Bittanti, A. J. Laub, and J. , The Riccati Equation, 2012.
DOI : 10.1007/978-3-642-58223-3

A. Björck and S. Hammarling, A Schur method for the square root of a matrix, pp.127-140, 1983.

D. Calvetti and L. , Application of ADI Iterative Methods to the Restoration of Noisy Images, SIAM Journal on Matrix Analysis and Applications, vol.17, issue.1, pp.165-186, 1996.
DOI : 10.1137/S0895479894273687

C. T. Chen, Linear System Theory and Design Third Edition, 1999.

J. F. Claerbout, Sylvester's matrix theorem, a section of Fundamentals of Geophysical Data Processing. Online version at sepwww, 1976.

G. D. Amico, Cosmology and perturbations in massive gravity, Arxiv, vol.12063617, 2013.

P. I. Davies and N. J. Higham, A Schur-Parlett Algorithm for Computing Matrix Functions, SIAM Journal on Matrix Analysis and Applications, vol.25, issue.2, pp.464-485, 2003.
DOI : 10.1137/S0895479802410815

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.660.7576

E. Deadman, N. J. Higham, and R. Ralha, Blocked Schur Algorithms for Computing the Matrix Square Root, Applied Parallel and Scientific Computing: 11th International Conference, pp.171-182, 2013.
DOI : 10.1007/978-3-642-36803-5_12

C. Deffayeta, J. Mourada, and G. , Zahariadea A note on symmetric vielbeins in bimetric, massive, perturbative and non perturbative gravities, Arxiv, vol.1208, p.4493, 2013.

F. Dellaert and M. Kaess, Square Root SAM: Simultaneous Localization and Mapping via Square Root Information Smoothing, The International Journal of Robotics Research, vol.23, issue.7, p.12, 2006.
DOI : 10.1007/978-3-642-97522-6

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.122.7443

L. Dieci, M. R. Osborne, and R. D. Russell, . I: Theoretical Aspects, SIAM Journal on Numerical Analysis, vol.25, issue.5, pp.1055-1073, 1988.
DOI : 10.1137/0725061

W. H. Enright, Improving the Efficiency of Matrix Operations in the Numerical Solution of Stiff Ordinary Differential Equations, ACM Transactions on Mathematical Software, vol.4, issue.2, pp.127-136, 1978.
DOI : 10.1145/355780.355784

M. A. Epton, Methods for the solution ofAXD???BXC=E and its application in the numerical solution of implicit ordinary differential equations, BIT, vol.13, issue.1, pp.341-345, 1980.
DOI : 10.1007/BF01932775

G. H. Golub, S. Nash, and C. F. Van-loan, A Hessenberg-Schur method for the problem AX + XB= C, IEEE Transactions on Automatic Control, vol.24, issue.6, pp.909-913, 1979.
DOI : 10.1109/TAC.1979.1102170

N. J. Higham, Functions of Matrices : Theory and Computation, 2008.
DOI : 10.1137/1.9780898717778

N. J. Higham, Stable iterations for the matrix square root, Numerical Algorithms, vol.15, issue.2, pp.227-242, 1997.
DOI : 10.1023/A:1019150005407

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.153.5966

N. J. Higham, Computing real square roots of a real matrix, Linear Algebra and its Applications, vol.88, issue.89, pp.405-430, 1987.
DOI : 10.1016/0024-3795(87)90118-2

N. J. Higham and L. Lin, A Schur???Pad?? Algorithm for Fractional Powers of a Matrix, SIAM Journal on Matrix Analysis and Applications, vol.32, issue.3, pp.1056-1078, 2011.
DOI : 10.1137/10081232X

P. Jain, C. Jin, S. M. Kakade, and P. Netrapalli, Global Convergence of Non-Convex Gradient Descent for Computing Matrix Squareroot. Arxiv 1507, p.5854, 2017.

C. R. Johnson, K. Okubo, and R. Reams, Uniqueness of matrix square roots and an application, Linear Algebra and its Applications, vol.323, issue.1-3, pp.1-3, 2001.
DOI : 10.1016/S0024-3795(00)00243-3

S. Julier and J. Uhlmann, A New Extension of the Kalman Filtering to Non Linear Systems, SPIE Proceedings Series, pp.182-193, 1997.

P. G. Kaminski, A. Bryson-jr, and S. Schmidt, Discrete square root filtering: A survey of current techniques, IEEE Transactions on Automatic Control, vol.16, issue.6, pp.727-736, 1971.
DOI : 10.1109/TAC.1971.1099816

P. Lancaster and L. Rodman, Algebraic Riccati equations, 1995.

A. Laub, A Schur method for solving algebraic Riccati equations, IEEE Transactions on Automatic Control, vol.24, issue.6, pp.913-921, 1979.
DOI : 10.1109/TAC.1979.1102178

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.325.369

S. G. Lee and Q. P. Vu, Simultaneous solutions of Sylvester equations and idempotent matrices separating the joint spectrum, Linear Algebra and its Applications, vol.435, issue.9, pp.2097-2109, 2011.
DOI : 10.1016/j.laa.2010.09.034

B. Meini, The Matrix Square Root from a New Functional Perspective: Theoretical Results and Computational Issues, SIAM Journal on Matrix Analysis and Applications, vol.26, issue.2, pp.362-376, 2004.
DOI : 10.1137/S0895479803426656

B. M. Morf and T. Kailath, Recent results in least square estimation theory, Annals of Economic and Social Measurement, vol.6, issue.3, 1977.

P. J. Psarrakos, On the nth roots of a complex matrix. The electronic, Journal of Linear Algebra, vol.9, pp.32-41, 2002.

M. Rhudy, Y. Gu, J. Gross, and M. R. Napolitano, Evaluation of Matrix Square Root Operations for UKF within a UAV GPS/INS Sensor Fusion Application, International Journal of Navigation and Observation, vol.34, issue.5, p.416828, 2011.
DOI : 10.1109/TCST.2006.880203

J. D. Roberts, Linear model reduction and solution of the algebraic Riccati equation by use of the sign function???, International Journal of Control, vol.10, issue.4, pp.677-687, 1980.
DOI : 10.1137/0114044

B. A. Schmitt, Perturbation bounds for matrix square roots and pythagorean sums, Linear Algebra and its Applications, vol.174, pp.215-227, 1992.
DOI : 10.1016/0024-3795(92)90052-C

V. Sima, Algorithms for Linear-Quadratic Optimization, Pure and Applied Mathematics, vol.200, 1996.

J. J. Sylvester, Sur les racines des matrices unitaires. Comptes Rendus de l, Académie des Sciences, vol.94, pp.396-399, 1882.

S. Sra, On the matrix square root via geometric optimization. ArXiv /1507, p.8366, 2015.
DOI : 10.13001/1081-3810.3196

URL : http://repository.uwyo.edu/cgi/viewcontent.cgi?filename=0&article=3196&context=ela&type=additional

R. Van-der-merwe and E. A. Wan, The square-root unscented Kalman filter for state and parameter-estimation, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221), 2001.
DOI : 10.1109/ICASSP.2001.940586

S. D. Wang, T. S. Kuo, and C. F. Hsu, Trace bounds on the solution of the algebraic matrix Riccati and Lyapunov equation, IEEE Transactions on Automatic Control, vol.31, issue.7, pp.654-656, 1986.
DOI : 10.1109/TAC.1986.1104370

Q. Wei, N. Dobigeon, and J. Tourneret, Fast Fusion of Multi-Band Images Based on Solving a Sylvester Equation, IEEE Transactions on Image Processing, vol.24, issue.11, pp.4109-4121, 2015.
DOI : 10.1109/TIP.2015.2458572

URL : https://hal.archives-ouvertes.fr/hal-01187314

J. Willems, Least squares stationary optimal control and the algebraic Riccati equation, IEEE Transactions on Automatic Control, vol.16, issue.6, pp.621-634, 1971.
DOI : 10.1109/TAC.1971.1099831