Controllability of a simplified time-discrete stabilized Kuramoto-Sivashinsky system

In this paper, we study some controllability and observability properties for a coupled system of time-discrete fourth- second-order parabolic equations. This can be regarded as simplification the well-known stabilized Kumamoto-Sivashinsky equation. Unlike continuous case, prove only relaxed inequality which yields $ \phi(\triangle t) $-controllability result. result tells that cannot reach exactly zero but rather small target whose size goes to 0 discretization parameter \triangle t 0. The proof relies on known Carleman estimate operators new fourth-order