Periodic zero-dynamics attacks for discrete-time second-order multi-agent systems

This article studies the zero-dynamics attacks (ZDAs) issue for discrete-time second-order multi-agent systems (MASs) in a directed interacting setting. It is shown that the consensus among interacting agents fails if the considered system is attacked by infinite number of ZDAs. As for the scenario of finite number of periodic ZDAs, the consensus value, specified by the weight of the initial conditions, can only be destroyed whenever the rooted agents are attacked, apart from the attack signal satisfying certain constraints. Based on this observation, we further give conditions upon which the consensus of MASs subject to finite number of ZDAs cannot be achieved. Finally, simulation examples associated with power networks are presented to support the devised setup.