Networked Consensus Agents Dynamics through Matrix Eigenvalue

The collective behavior system depends strongly on the efficiency of communication paths, in other words, network topology. Network connectivity affects the properties of networked agents. Synchronous behavior is also affected by the network structure. A consensus problem is also related to the problem of synchronization. A consensus algorithm is an interaction rule that specifies the information exchange between an agent and all of its neighbors on the network. A class of local control laws is investigated for a collection of agents that result in global order their motion in convergence of their movement to a common. In large groups of agents the information sharing should be local in some sense, due to energy limitation, reliability, and other constraints. However, local information exchange limits the speed of convergence of such protocols. A consensus protocol is an iteractive method that provides the group with a common coordination variable. In this paper, we describe the occurrence of flocking behavior and the underlying connection between agents. The occurrence of flocking behavior in the synchronization of networked agents is directly associated with the connectivity properties of the interconnection network. Each node of the network represents a dynamical system. Individual systems are coupled according to the network topology. It is possible to think about the network topology through local control action by exploiting the graph theoretic properties of the agent networks. We consider the network by the Laplacian matrix eigenvalue viewpoint.