Leader-follower consensus of multi-agent systems over finite fields via semi-tensor product of matrices

This paper investigates the leader-follower consensus problem of multi-agent systems with time-delay over finite fields by using the semi-tensor product of matrices. Firstly, the dynamics of leader-follower multi-agent systems with time-delay is converted into an equivalent algebraic form. Secondly, based on the algebraic form, a necessary and sufficient condition is presented for the leader-follower consensus problem of multi-agent systems with time-delay over finite fields. Finally, based on the analysis of leader-follower multi-agent systems with time-delay, we add a control into system and present a necessary and sufficient condition for the leader-follower consensus problem of multi-agent systems with time-delay over finite fields.