Investigation Of Robust Adaptive Synchronization Of Uncertain Complex Networks With Time-varying Delays

Recently,technological revolutions of complex networks have received a remarkable attention in various fields.In the dissertation,four types of uncertain complex networks which contain coupling time-varying delays,nodes delays,and the uncertainties of both the inner and the outer coupling matrix are introduced.In order to research the further study of the robust adaptive synchronization,some deductive synchronization criteria of the complex dynamical networks mentioned above are raised by employing the Lyapunov stability theory,the adaptive control theory,the robust principle and the maxtix analysis technology.The mian innovative work and key points can be summarized as follows.(1)The robust adaptive synchronization of the complex network contianing coupling time-varying delays and nodes delays has been investigated.The complex model studied above contains not only the time-varying,but also the coupling delays and nodes delays,which fully characterizes the special dynamics of the complex networks in the real-world.Based on the Lyapunov stability theory,the matrix analysis techniques and the adaptive control theory,we construct a reaonable Lyapunov-Krasovskii functional,and give the synchronization criterion of the complex network.And then give the numerical simulations of the networks with time-varying Lorenz chactic systems.The results of the study show that thecomplex networks with coupling time-varying delay and nodes delay can achieve synchronization with the adaptive controller.(2)The robust adaptive synchronization of the complex network contianing coupling time-varying delays,nodes delays and the uncertainties of coupling matrixes have been investigated.The uncertainties are generally exist because of that the real control process can not be exactly expressed with the mathematical model in the modeling process.So it can be better used in the real system if we consider the uncertainties of the outer coupling matrix and inner coupling matrix.We also give the synchronization criterions of the two types of complex networks and make the theoretical and numerical simulation verification.(3)The robust adaptive synchronization of the uncertain complex network contianing coupling time-varying delays,nodes delays and the uncertainties of both the inner and the outer coupling matrix has been investigated.We give the synchronization criterion of the complex network and give the theoretical verification.The numerical simulations for the networks of time-varying Lorenz chactic systems are then provided to demonstrate the effectivenee and feasibility of proposed results and previous schemes for accuracy.In the end,the results of the dissertation are then summarized and futher research topics are recommeded.