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

Abstract

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.