Year: 2026
Type: article
Abstract: 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.
Source: Axioms
Authors: Airen Zhou, Yun Zhu, Changbin Zhao
Institution: Guizhou University of Finance and Economics
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,896
Awards: G1477469074, G4046957608
OpenAlex ID: W7154630474