Consistency of Multi-Agent Systems with Lur'e Nonlinearity in a Directed Switching Topology

This paper study a directed topology. Compared with the conclusions of the existing undirected topology, the requirements of the communication topology are greatly reduced and more general. The designed control protocol only utilizes the information of the neighbor agents. In order to convert the consensus problem under the switching topology into a stability problem of a low-dimensional switching system, the special property of the directed graph Laplacian matrix is used to decompose it, then use the linear transformation in a particular form. Then the Lyapunov function method combined with the linear matrix inequality method is used to analyze the stability of the system. The feedback matrix of the dynamic consensus controller is given, and the average dwell time condition is obtained. The results show that the proposed method can achieve the consensus of the Lur'e type nonlinear multi-agent system under arbitrary switching topology conditions.