Unconditionally stable scheme for Riccati equation

Free access article

Issue		ESAIM: PROC Volume 8, 2000 Contrôle des systèmes gouvernés par des équations aux dérivées partielles


Page(s)		39 - 52
DOI		10.1051/proc:2000003

ESAIM: Proc., 2000, Vol. 8, pp. 39-52
DOI: 10.1051/proc:2000003

Unconditionally stable scheme for Riccati equation

François Dubois¹ and 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

Abstract
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.

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