Controllability of Multi-agent Systems over Finite Fields Based on High-order Fully Actuated System Approaches

In this paper, the controllability of multi-agent systems over finite fields is studied based on the high-order fully actuated (HOFA) system approaches. The HOFA system over finite fields is presented first. The necessary and sufficient conditions for the controllability of linear systems over finite fields are given in terms of the controllability matrix. It is proved that a linear system over a finite field is controllable if and only if it can be transformed into an HOFA system. Finally, an example is shown to verify the validity of the main results of this paper.