Homographic scheme for Riccati equation

François Dubois (1) , Abdelkader Saïdi (2)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 IRMA - Institut de Recherche Mathématique Avancée

In this paper we present a numerical scheme for the resolution of matrix Riccati equation, usualy used in control problems. The scheme is unconditionnaly 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.

Mots clés: control problems; stability; ordinary differential equations; stability.

Domaines: Analyse numérique [math.NA]

François Dubois, Abdelkader Saïdi. Homographic scheme for Riccati equation. 2000. ⟨hal-00554484v2⟩