Controllability results of discrete boundary control system in Banach spaces

In this paper, we study the boundary controllability of the discrete-time control system in Banach spaces. The aim is to establish sufficient conditions for the existence and uniqueness of solutions, as well as for the approximate controllability of a discrete-time boundary control system. The form of the solution to the considered system and its existence and uniqueness are obtained using non-linear functional analysis, theory of difference equations, semigroup theory and contraction mapping principle. Furthermore, we achieve the approximate controllability results through a sequential approach. In the end, we present some examples to illustrate the application of these analytical results.