Research On Synchronization Of Stochastic Jump Complex Networks System

Complex networks system model is ubiquitous in human production and life.With the rapid development of the information age,its application becomes increasingly widespread.The signal transmission process in complex networks system sometimes exists lags,which has a certain impact on the stability and performance index of the system.So considering the complex networks system with time delay,we can more accurately reflect the characteristics of the whole network.In addition,synchronization behavior is one of the typical dynamic behaviors in complex networks system,and it is common in nature.Therefore,it is more valuable in theory and practice to study the synchronization control of complex network systems with time-delay.In this paper,the synchronization control of complex networks system with Markov jump,bounded Markov jump and semi-Markov jump are studied.The main research work is as follows:Firstly,based on the sampled-data control theory,the synchronization of a class of master-slave complex networks system with Markov jump and mixed delay is studied.By constructing a Lyapunov-Krasovskii functional,using integral inequality with higher accuracy,and combining with the convex combination method,the synchronization criterion of the system satisfying the mixed H_∞/passive performance is established.Secondly,the problem of passive synchronization for a class of complex networks system with bounded Markov jump and coupling time-varying delay is discussed.By using the fault-tolerant sampled-data controller,a Lyapunov-Krasovskii functional with triple integral term is constructed.The sufficient conditions for the system to be synchronous and passive are obtained by combining integral inequality,free weighting matrix and Newton-Leibniz formula.When the actuator fails,the closed-loop error system is passive synchronous.It not only complements the basic theory of fault-tolerant sampled-data control of complex networks system,but also extends it to the study of synchronization theory for complex network systems with bounded Markov jumps.Finally,the exponential synchronization of complex networks system with semi-Markov jump topology is considered.A memory sampled-data controller is designed.By constructing the Lyapunov-Krasovskii functional related to the sampling information,and using the stability theory analysis and basic knowledge of inequality,the exponential synchronization criterion of the system with mixed H_∞/passive performance is given.And it is further extended to the study of the synchronization theory for complex network system with semiMarkov jump.The established complex network model is more complex and more realistic.