Impulse output rapid stabilization for heat equations

The main aim of this paper is to provide a new feedback law for the heat equations in a bounded domain $\mathrm{\Omega }$ with Dirichlet boundary condition. Two constraints will be compulsory: First, The controls are active in a subdomain of $\mathrm{\Omega }$ 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.