Connection between the 3-Block Generalized Riccati Equation and the Standard Riccati Equation

Mohamed Darouach (1) , Michel Zasadzinski (1) , André Bassong Onana (1)

1 CRAN - Centre de Recherche en Automatique de Nancy

In a recent paper, Nikoukhah et al. (IEEE TAC 1992) developed a maximum likelihood descriptor Kalman filter (DKF) the properties of which are governed by a 3-block generalized Riccati difference equation (GRDE). The convergence of this GRDE has been studied and the generalization of the eigenvector approach to solving the associated generalized algebraic Riccati equation (GARE) has been carried out. In this paper, we connect the GRDE to the standard Riccati equation in order to point out Nikoukhah's results from well known results obtained in the standard Kalman filtering. Moreover, while the previous study made by (IEEE TAC 1992) provides only sufficient conditions on the convergence and stability of the 3-block DKF, the relationship established herein allows us to derive necessary and sufficient conditions. In addition, several descriptor Kalman filtering problems can be treated as in the standard case.

Mots clés: Descriptor systems; Discrete time; Kalman Filter; Generalized Riccati difference equation; Generalized Algebraic Riccati equation

Domaines: Automatique / Robotique

Mohamed Darouach, Michel Zasadzinski, André Bassong Onana. Connection between the 3-Block Generalized Riccati Equation and the Standard Riccati Equation. IEEE Transactions on Automatic Control, 1994, 39 (8), pp.1755-1758. ⟨hal-00098132⟩