A generalization of the Kalman rank condition for time-dependent coupled linear parabolic systems

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

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

In this paper we present a generalization of the Kalman rank condition for linear ordinary differential systems to the case of a systems of n coupled parabolic equations (posed in the time interval (0, T) with T > 0) where the coupling matrices A and B depend on the time variable t. To be precise, we will prove that the Kalman rank condition rank [A|B](t0) = n, with t0 in [0, T], is a sufficient condition (but not necessary) for obtaining the exact controllability to the trajectories of the considered parabolic system

Domaines: Equations aux dérivées partielles [math.AP]

Cédric Dupaix, F. Ammar Khodja, A. Benabdalah, M. Gonzalez-Burgos. A generalization of the Kalman rank condition for time-dependent coupled linear parabolic systems. Diff. Equ. and Appl., 2009, 1 (3), pp.427-457. ⟨hal-00472533⟩