Impulsive Observer-Based Control in Clustered Networks of Linear Multi-Agent Systems

This article addresses the problem of consensus in networks divided into subnetworks (also called clusters), where each node of the network graph represents an agent with linear dynamics. Each subnetwork is represented by a directed graph. Moreover, the agents in each cluster cannot communicate with agents from other clusters, except one single agent of each subnetwork, which is called a leader. These leaders interact some instant times via a fixed and strongly connected directed graph. An impulsive observer-based control protocol is proposed. Based on this proposed protocol, the collective network dynamics of multi-agent systems is described in the term of hybrid systems. The characterization of the global consensus value of this kind of networks is analyzed. Secondly, we show that the problem of consensus design for clustered networks can be indirectly solved by considering the stability of an equivalent system. Then, a sufficient condition for the asymptotical stability of this equivalent system is proposed. Finally, an algorithm properly selects the interaction network of the leaders, feedback gain, observer gain matrices, and coupling weights. This allows agents in the clustered network to enclose a prior fixed target. Simulation results are given to demonstrate the effectiveness of the theoretical results.