Finite-field consensus networks with multi-communication channels and time-delays

This paper investigates the consensus problem of multi-communication networks with time-delays over finite fields. Firstly, the constant delay case is studied. Based on the algebraic topology and the graph theory, some criteria, guaranteeing that finite-field networks with multi-communication channels and constant time-delays achieve finite-field consensus, are derived. Then the inverse recursion subspaces are studied, revealing that the finite-field consensus problem can be determined by a small part of states. Along the lines of constant time-delays networks, the finite-field consensus of multi-communication networks with time-varying bounded delays is discussed. And the distinguish condition of the method using a union graph is given. Finally, a numerical example is provided to illustrate the effectiveness of the proposed results.