Stability And Synchronization Of Severval Classes Complex Networks

Stability and synchronization of complex networks have been paid more and more attention.Neural networks and multi-agent systems are two kinds of complex networks in nature,engineering and technology.Memristive neural networks bring hope for the simulation of human brains and the construction of neural computers.Stability and synchronization of memristive neural networks is the basis of their applications.Consensus(synchronization)of multi-agent systems has been widely used in the field of exploring the collective behavior of animals,distributed control of multi robots,and distributed control of multiple unmanned aerial vehicles.Based on functional differential equations,matrix theory and linear matrix inequalities,the stability and synchronization problems of two kinds of complex networks mentioned above are discussed.The main contents and contributions are given as follows:(1)Stability of delayed memristive neural networks is considered.A new memristive Hopfield neural networks model is proposed.That is,memristors are viewed as continuous and time-varying parameters,and memristive neural networks are modeled as neural networks with continuous and time-varying parameters.Stability conditions of delayed memristive neural networks are derived using Lyapunov-Krasovskii functional and linear matrix inequalities.Based on average dwell time,mode-dependent average dwell time,Lyapunov-Krasovskii functional and linear matrix inequalities approaches,conditions are derived to design a switching signal and guarantee the stability of switched memristive neural networks with delays.(2)Master-slave synchronization of delayed memristive Hopfield neural networks is considered.A new approach is proposed to solve the problem.That is,synchronization of delayed memristive Hopfield neural networks is converted into quasi-synchronization of delayed neural networks with continuous and time-varying parameters mismatches.Criteria of quasi-synchronization for the systems are derived by Lyapunov-Krasovskii functional,linear matrix inequalities and Halanay inequality.It is shown that quasi-synchronization can be achieved if the feedback gain is larger than a threshold.(3)Several kinds of multi-agent systems are considered,such as linear multi-agent systems,switched linear multi-agent systems.Based on observer and sampled-data,consensus protocols are proposed.Consensus criteria and an algorithm are obtained using matrix theory and sampled control theory for linear multi-agent systems.Consensus criteria of discrete-time switched linear multi-agent systems are given to design the feedback gain matrices and the observer gain matrices by average dwell time,linear matrix inequalities and sampled control theory.(4)Note that a chaotic Jerk circuit is a third-order nonlinear system.Consensus of third-order nonlinear multi-agent systems is first proposed.The consensus problem is converted to a stability problem of an error system.Consensus criteria are given by proposing a new Lyapunov function.It is shown that consensus can be always achieved for a sufficiently large feedback gain.