Research On Finite-time Synchronization Of Two Classes Of Complex Networks With Time-varying Delays

Complex dynamical networks consist of a large number of interacting dynamical n-odes connected by links have received much attention from various fields like mathematics,biology,sociology,and economic science.Synchronization,which means the dynamical behaviors of coupled nodes in a network achieve the same state both in time and spa-tial,according to the time of achieving synchronization,it can be divided into two parts:asymptotic synchronization and finite-time synchronization.The former is only achieved when time goes to infinity,while the latter's complete synchronization of coupling network is achieved in a setting time.The most existing literature is about asymptotic synchro-nization.Unfortunately,finite-time synchronization in engineering fields,especially in secure communication can largely improve the efficiency and confidentiality in recovering the transmitted signals,and more than that,it has better robustness and disturbance rejection against uncertainties compared to asymptotic synchronization,which attracts large attention from researchers in recent years.Therefore,finite-time synchronization of complex networks using different controllers was mainly considered in this paper,which is organized as following several aspects:Firstly,we introduce significance of research complex networks and its wide appli-cation,serious kinds of synchronizations of complex networks and the development of finite-time synchronization.In the second place,we briefly state some knowledge of graph theory,in addition,some necessary definitions like finite-time synchronization and lemmas such as finite-time stability theory are introduced in this section and will be used throughout the wholepaper.In the third chapter,finite-time synchronization of Markovian jump complex net-works with time-varying delays is discussed.Based on the finite-time stability theo-rem and matrix inequality,by designing proper controllers and constructing Lyapunov-Krasovskii functional,the sufficient conditions to achieve finite-time synchronization of the complex networks are derived,and estimate the setting time according to the finite-time stability theorem.At last,a numerical example is proposed to verify the effectiveness of the theoretical result.Next,finite-time synchronization of complex dynamical network with time-varying delay are considered.Based on the strict analytical techniques,we design a simple con-troller which only include error state and its sign function and obtain sufficient conditions for finite-time synchronization using a Lyapunov functional consisted of error state's one norm.Besides,the upper bound of synchronization time is estimated and some corre-sponding numerical simulations like networks consisted of nodes whose dynamical be-havior is chua's circuit can also be presented to demonstrate the correctness of obtained results.At last,we sum up the paper,reviewing the existing literature which is about the research of corresponding network and its control methods,meanwhile,giving the future work.