Study on Consensus of the Forth-Order Discrete-Time Multiagent System in Directed Networks

In this paper, we are concerned with the consensus of the forth-order discrete-time multiagent system in directed networks. First, by defining a group of new variables, the multiagent system is converted to the corresponding reduced order system. Based on the stability of the reduced order system, we discuss the consensus of the original multiagent system. Then, two necessary and sufficient conditions for the consensus of the forth-order discrete-time multiagent system are established by using the related knowledge of algebraic graph theory and matrix theory. Compared with the existing results, the obtained conditions of this paper are more extensive. In order to reduce the number of information exchange between agents, we use event-triggered mechanism to deal with the consensus of the multiagent system. Furthermore, Zeno behavior of multiagent system will not make an appearance due to the reasonable design of the triggering function. A numerical example is finally given to demonstrate the effectiveness of theoretical results.