Controllability of discrete-time multi-agent systems based on absolute protocol with time-delays

This paper investigates complete controllability and structural controllability of discrete-time multi-agent systems (MASs) under a leader-follower framework with time-delays based on absolute protocol, respectively, where both a single time-delay and multiple time-delays are investigated. By using the equivalent augmented systems without time-delays, some new graph-theoretic and algebraic characterizations are respectively built for complete controllability and structural controllability depending on communication flows of MASs. In addition, the simulation results are given.