On The Cluster Consensus And Stabilization Of Complex Networks

This thesis studies the dynamics of complex networks. At first, the cluster consen-sus of networks with clustering structures is investigated. For discrete time, continuous time and second order systems, the criteria are derived to guarantee cluster consensus. A new definition of cluster consensus is given, which contains two aspects:intra-cluster synchronization, and inter-cluster separation. To realize inter-cluster separation, ex-ternal inputs are imposed to nodes. The influence of the topological structure on intra-cluster synchronization and the role that external inputs play on inter-cluster separation are carefully studied. Inspired by the roles of spanning tree and Hajnal inequality on consensus problem of complex networks, a concept of cluster spanning is proposed and the Hajnal inequality for the clustering case is extended. Based on the product theory of stochastic matrices and cluster Hajnal inequality, sufficient con-ditions based on topological structure are derived to guarantee intra-cluster synchro-nization. The dynamical properties of nodes are given by external inputs, to realize inter-cluster separation, agents in the same cluster have the same inputs and agents in different clusters have different inputs. Secondly, the stability of pinning control on the complex networks with stochastically switching topologies and controller-node sets is investigated. Two scenarios are considered here. First, it is proved that if each subsystem in the switching system, i.e. with the fixed coupling, can be stabilized by a fixed pinning controller-node set, and in addition, the stochastically switching is sufficiently slow, then the time-varying dynamical system is stabilized. Second, it is concluded that if the system with the average coupling and pinning gains can be stabilized and the switching is sufficiently fast, the time-varying, system is stabilized. Thirdly, as an application of the stability of complex networks, the power of moving target defense via cyber epidemic dynamics is characterized. The theoretical analysis on the existence of optimal MTD is presented and the algorithms are given to deploy the optimal MTD.