Group controllability of discrete‐time second‐order multi‐agent systems with two‐time‐scale feature

Abstract This study investigates the group controllability of discrete‐time second‐order multi‐agent systems (MASs) with two‐time‐scale feature. The paper first provides a definition of the group controllability of discrete‐time second‐order MASs with two‐time‐scale feature. In view of the ill‐posedness problem that occurs when the classical control theory is used directly to manage the controllability of two‐time‐scale MASs with a singular perturbation parameter, we adopt a singular perturbation method based on iteration and approximation to decompose two‐time‐scale MASs into fast‐time‐scale and slow‐time‐scale subsystems. Subsequently, by combining the Kalman rank criterion and matrix theory knowledge, several additional easy‐to‐operate controllable criteria are proposed for these MASs. The validity is then demonstrated through simulations, and the influence of the singular perturbation parameter on the group controllability of discrete‐time second‐order MASs is discussed. This research complements existing situations in which only first‐order agents are considered.