Synchronization Of Complex Dynamical Networks With Non-Identical Coupling Delays And Switching Topologies

Synchronization is the very important dynamical behavior of the complex dynamic networks. In real networks, the link failures or new creations often occur, so the network topologies change discontinuously that causes switching network topologies. Since the existence of time delays in real systems will result in the deterioration of the system performance, the research of complex networks with time delays and switching topologies is of significance.By constructing the piecewise Lyapunov-Krasovskii functional, adopting the average dwell time approach of the switched system stability theory and free weight matrix technology of time delayed systems, the synchronization is investigated for the complex networks with non-identical coupling delays and switching topologies. The main research results are listed as following:(1) By means of the switched system theory with the average dwell time and free weight matrix approach, the exponential synchronization is investigated for the complex dynamical networks with non-identical time-varying coupling delays and switching topologies under two conditions:one is that all subnetworks are self-synchronizing, the other is that some subnetworks are non-synchronizing. The delay-dependent sufficient conditions are derived to ensure the exponential synchronization of the entire network of which all sub-networks are self-synchronizing. Then the results are extended to the complex network where some sub-networks are non-synchronizing. For the latter, the inferior bound of the ratio between total active time of self-synchronizing and non-synchronizing is given to guarantee the exponential synchronization of the entire network as well as the average dwell time.(2) The exponential synchronization problem is considered for impulsive complex networks with non-identical fixed coupling delays and switching topologies. The delay-dependent sufficient conditions and switching signals are proposed to guarantee the exponential synchronization of entire network with respect to all sub-networks self-synchronizing and some sub-networks non-sychronizing. (3) The design problem of decentralized controllers is considered for the complex networks with non-identical time-varying coupling time delays and switching topologies. The delay-dependent sufficient conditions are derived to ensure the exponential synchronization of the entire network by decentralized control. Based on the above, the design method of the decentralized controllers is presented with parameter adjustment approach.