In this paper, we investigate controllability for both linear and nonlinear Hahn difference equations, whose nonlinear terms are given by involving maxima. Introducing a Grammian matrix, we derive a necessary and sufficient condition characterizing controllability for linear Hahn difference control systems. For the nonlinear case with maxima, we construct an appropriate control input that allows reformulation as a fixed-point problem, enabling the use of fixed-point techniques. In particular, Krasnoselskii’s fixed point theorem is employed to obtain a controllability result. Finally, two examples are given to demonstrate our theoretical findings, including computation of the required control functions and the inverse of the Grammian matrix.
Zhou et al. (Thu,) studied this question.