Synchronization Analysis Of Complex Networks Based On Sampled-data Control

Complex networks have received great attention due to their wide application.Synchronization is the focus of many subjects in the study of the dynamic behavior of complex networks.Because there are many uncertainties in the network such as external disturbance and parameter fluctuation,the stability of the system will be destroyed.Therefore,it is of great significance to study the synchronization of uncertain complex networks.At the same time,due to the external disturbance,system mutation,parameter uncertainty and individual differences and other factors may lead to the heterogeneity of network system,heterogeneous network is widely existed in practical applications.Therefore,the synchronization of heterogeneous networks is worth further study.Considering that sampled-data control can reduce signal transmission and communication cost,this paper studies the synchronization of a class of time-delay heterogeneous networks based on sampled-data control,the synchronization of uncertain complex networks based on sampled-data control and input saturation,and the synchronization of heterogeneous complex networks based on memory samped-data control.The main research results are as follows:(1)This paper discusses the quasi-synchronization problem in nonlinear heterogeneous complex dynamical networks with time-varying delays and sampled-data control with input-delay Firstly,the Lyapunov-Krasovskii functional with more information and the sampling interval delay information was constructed.Then,based on the Lyapunov-Krasovskii functional approach,integral inequality and linear matrix inequality method,by introducing a leader,sufficient criteria are obtained to guarantee quasi-synchronization for nonlinear heterogeneous dynamical networks.All heterogeneous followers can track the leader within a bounded range.And the upper bound of the quasi-synchronization error can be estimated.Finally,simulation examples are provided to illustrate the theoretical results.(2)This paper discusses the synchronization problem of nonlinear uncertain complex dynamical networks with sampled-data and input saturation.Firstly,establish a nonlinear and uncertain complex network model,and secondly,a leader is introduced to design a sampled-data control protocol with input saturation.By constructing an appropriate time-dependent Lyapunov functional and applying the stability theory,integral inequality method and the linear matrix inequality method,it is proved that the nonlinear uncertain complex dynamical networks can achieve synchronization under certain conditions,that is every follower can track the leader,and the sufficient criteria for achieving synchronization of nonlinear uncertain complex networks is derived.Finally,simulation examples are provided to verify the effectiveness and validity of the theoretical results.(3)This paper investigates the quasi-synchronization problem for a class of heterogeneous dynamical networks based on a non-fragile memory sampled-data controller.Considering the effect of controller gain fluctuation and communication delay,a sampled-data control scheme with norm-bounded uncertainty and a constant signal transmission delay is designed.By introducing a leader,the heterogeneous complex delayed networks can be transformed into the corresponding error systems with bounded disturbances.A sufficient criterion to ensure that the error system can be exponentially stable and converge to a bounded region is established by the Lyapunov-Krasovskii function approach.Based on the criterion,the sampled-data control gain matrix is designed.Finally,the effectiveness of the theoretical results is verified by numerical simulation,and the advantages of memory sampled-data control are proved by simulation examples.