Second‐order controllability of two‐time‐Scale discrete‐time multi‐agent systems

In this study, the controllability of multi-agent systems with second-order dynamic under discrete-time model, which evolve on two time scales. The authors first characterise the systems by difference equations with a singular perturbation parameter. Then, in order to get rid of the singular perturbation parameter, they split the systems into a slow subsystem and fast subsystem based on the iterative method and approximate approach. Moreover, according to matrix theory, they deduce a lot of necessary and/or sufficient controllability criteria of the systems. In particular, a second-order controllability criterion only depending on the eigenvalues of matrices is proposed, which is more easy-to-use and efficient. A simulation example is lastly given to clarify the validity of all theoretical results.