Carleman estimates for time-discrete parabolic equations and applications to controllability

International audienceIn this paper, we prove a Carleman estimate for a time-discrete parabolic equation in which the large parameter is connected to the time step of the discretization scheme. This estimate is then used to obtain a relaxed observability estimate that yields some controllability results for linear and semi-linear time-discrete parabolic equations. We also discuss the application of this Carleman estimate to the controllability of coupled systems