Geodesic
Unconditionally stable scheme for Riccati equation
François Dubois1 ; Abdelkader Saïdi2
1 Conservatoire National des Arts et Métiers, 15 rue Marat, F-78 210 Saint Cyr l'Ecole, France
2 Institut de Recherche Mathématique Avancée, Université de Louis Pasteur de Strasbourg, 7 Rue René-Descartes, 67084 Strasbourg Cedex, France
ESAIM. Proceedings, Tome 8 (2000), pp. 39-52 Cet article a éte moissonné depuis la source EDP Sciences

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In this communication we present a numerical scheme for the resolution of matrix Riccati equation used in control problems. The scheme is unconditionnally stable and the solution is definite positive at each time step of the resolution. We prove the convergence in the scalar case and present several numerical experiments for classical test cases.
DOI : 10.1051/proc:2000003

François Dubois 1 ; Abdelkader Saïdi 2

1 Conservatoire National des Arts et Métiers, 15 rue Marat, F-78 210 Saint Cyr l'Ecole, France
2 Institut de Recherche Mathématique Avancée, Université de Louis Pasteur de Strasbourg, 7 Rue René-Descartes, 67084 Strasbourg Cedex, France 
@article{EP_2000_8_a2,
     author = {Fran\c{c}ois Dubois and Abdelkader Sa{\"\i}di},
     title = {Unconditionally stable scheme for {Riccati} equation},
     journal = {ESAIM. Proceedings},
     pages = {39--52},
     year = {2000},
     volume = {8},
     doi = {10.1051/proc:2000003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc:2000003/}
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François Dubois; Abdelkader Saïdi. Unconditionally stable scheme for Riccati equation. ESAIM. Proceedings, Tome 8 (2000), pp. 39-52. doi: 10.1051/proc:2000003

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