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

Cédric Dupaix (1) , F. Ammar Khodja , A. Benabdallah , M. Gonzalez-Burgos

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)

We present a generalization of the Kalman rank condition to the case of n × 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.

Domaines: Equations aux dérivées partielles [math.AP]

Cédric Dupaix, F. Ammar Khodja, A. Benabdallah, M. Gonzalez-Burgos. A Kalman rank condition for the localized distributed controllability of a class of linear parabolic systems. Journal of Evolution Equations, 2009, 9 (2), pp.267-291. ⟨10.1007/s00028-009-0008-8⟩. ⟨hal-00474057⟩