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

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.