  The main aim of this paper is to provide a new feedback law for the heat
equations in a bounded domain $\Omega $ with Dirichlet boundary condition. Two
constraints will be compulsory: First, The controls are active in a subdomain
of $\Omega $ and at discrete time points; Second, The observations are made in
another subdomain and at different discrete time points. Our strategy consists
in linking an observation estimate at one time, minimal norm impulse control,
approximate inverse source problem and rapid output stabilization.
