A Kalman rank condition for the localized distributed controllability of a class of linear parabolic systems

Farid Ammar-Khodja (1) , Assia Benabdallah (2) , Cédric Dupaix (1) , Manuel Gonzalez-Burgos (3)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
2 LATP - Laboratoire d'Analyse, Topologie, Probabilités
3 Universidad de Sevilla = University of Seville

We present a generalization of the Kalman rank condition to the case of $n\times n$ linear parabolic systems with constant coefficients and diagonalizable diffusion matrix. To reach the result, we are led to prove a global Carleman estimate for the solutions of a scalar $2n-$order parabolic equation and deduce from it an observability inequality for our adjoint system.

Mots clés: Kalman condition; control; observability; Carleman estimates; reaction diffusion systems

Domaines: Equations aux dérivées partielles [math.AP]

Farid Ammar-Khodja, Assia Benabdallah, Cédric Dupaix, Manuel Gonzalez-Burgos. A Kalman rank condition for the localized distributed controllability of a class of linear parabolic systems. 2008. ⟨hal-00290867⟩