Consensus of finite-field networks with switching topologies and linear protocols

This paper investigates the consensus of finite-field networks with switching topologies and linear protocols by using the semi-tensor product (STP) method, and presents a number of new results. First, an algebraic form of finite-field networks with switching topologies and linear protocols is obtained via STP. Second, based on the algebraic form and the switching point reachability, a necessary and sufficient condition is presented for the consensus of finite-field networks under arbitrary switching signal. Finally, an illustrative example is given to verify the obtained new results. The study of the illustrative example shows that the new results presented in this paper are very effective in the consensus analysis of finite-field networks with switching topologies and linear protocols under arbitrary switching signal.