Fault Tolerant Synchronization For A General Complex Dynamical Networks With Random Delays

With the development of computer and internet technology,nowadays the complex dynamical networks have many applications in modern life such as power grids,communications,traffic network and so on.Synchronization as one of typical collective behaviors of a dynamical network has been increasingly focused since the latest decades.The ideal coupled complex dynamical network will not always exist in practical systems,and various unexpected factors disturb the synchronization of complex dynamical networks,such as the time delay during the information transmission between nodes,the faults of network couplings and so on.Therefore,it is necessary to establish the complex dynamical network model conforming to the actual situation,then to adopt the most effective control strategy to realize the synchronization of the complex dynamical networks with different faults.This paper aim to study the synchronization of the complex dynamical networks with random delays against different faults,which is of great significance to practical application of the complex dynamical networks.The main contributions are listed as follows:Firstly,we study the fault complex dynamical network with random delays,and considering the network internal coupling faults between nodes,then fault tolerant control strategy is adopted to design the external controller.Based on the Lyapunov stability theory and stochastic analysis,a novel passive fault tolerant synchronization criteria is derived in form of linear matrix inequalities(LMI),which realizes the synchronization of a complex dynamical network.Secondly,when realizing the synchronization of a complex dynamical network with random delays and network coupling faults by adding the external controllers,the actuator faults occurred in the external controllers must be considered,which lead to the complex dynamical network out of synchronization.Based on the fault tolerant control strategy and Lyapunov stability theory,the fault tolerant controller is proposed and obtain the synchronization criterion in form of linear matrix inequalities(LMI)for the complex dynamical network with random delays and the actuator faults.Finally,a large-scale complex dynamical network with random delays against network internal coupling faults is investigated.Due to the large-scale network contains a large number of nodes,it is difficult for us to add the fault tolerant controllers to the all nodes to achieve the synchronization of the complex dynamical network.Thus combining pinning control method with fault tolerant control method,we give the minimum number of fault tolerant controllers added to the networknodes and fault tolerant synchronization criterion by using Lyapunov stability theory,which realize the synchronization of a large-scale complex dynamical network with random delays against network coupling faults finally.