Group controllability of two-time-scale discrete-time multi-agent systems

In this paper, we address the group controllability issue for discrete-time multi-agent systems (MASs) with two-time-scale feature. Since the existence of singular perturbation parameter in modeling the two-time-scale MASs will cause ill-posedness problems, we decouple the MASs into fast and slow subsystems by using the iterative and approximate methods, and then eliminate the singular perturbation parameter. By using matrix theory, we propose a lot of necessary and/or sufficient conditions of group controllability, where some easy-to-use criteria are determined only by eigenvalues of matrices. Lastly, a simulation example is given to illustrate the effectiveness of the proposed theoretical results.