Controllability of Hahn Difference Equations with Maxima

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.