| Complex systems have long been embedded in many areas of social activity and are well known as communication systems,neural systems,transport systems,etc.These complex systems have a large number of members and exhibit complex dynamics,and are often described in terms of complex networks.Among the many dynamics of complex networks,the synchronization of nodes is of great practical importance,and the relevant research theories can guide the good formation of UAVs and the cooperative operation of power networks.In a realistic environment,complex networks are inevitably affected by external disturbances,and robust H? control is a better way to describe and deal with how to measure the impact of external disturbances on the networks.At present,there are many control methods used to study the problem of robust H? synchronization,such as feedback control,pinning control,adaptive control,etc.Among them,impulsive control,as a discontinuous method,can effectively reduce the control cost and enhance the robustness of the networks by exerting its effect on the network only at some discrete moments,which has attracted widespread attention from scholars.In this paper,we consider the influence of communication delay and external disturbances on the characteristics of complex networks,and investigate the problem of robust H? impulsive synchronization for three types of complex networks with multi-weights,uncertainty and topological switching respectively.We combine the knowledge of Lyapunov stability theory,matrix theory and mathematical induction by means of impulsive control,and give the relevant criteria for achieving robust H? impulsive synchronization for the above three types of complex networks,and The correctness of the criterion is verified by numerical examples.In this paper,we focus on the following aspects:First,the robust H? impulsive synchronization problem of complex network with multi-weights is investigated.According to the different coupling forms inside the network nodes,the complex network with multi-weights is divide into several single-weighted sub-networks with different properties.The stability and 2L-gain of the synchronization error system are analyzed by designing a suitable impulsive controller for control,and the related criterion for the network to achieve robust H? impulsive synchronization are given in terms of Linear Matrix Inequalities(LMIs).Next,the robust H? impulsive synchronization problem of uncertain complex network with multi-weights is investigated considering the uncertainty arising from the external environment and human factors.By designing a suitable impulsive controller and combining Lyapunov stability theory,mathematical induction method,matrix theory and other related knowledge,sufficient conditions for robust H? impulsive synchronization of network is given,and the validity of the conclusion is verified by numerical simulation results.Finally,the robust H? impulsive synchronization problem of complex network with multi-weights under topology switching is studied.The network is split according to the different communication delays during the information transmission between network nodes.The criterion for achieving robust H? impulsive synchronization under arbitrary topology switching rules for complex network with multi-weights is given.Unlike the existing literature where the topology switching behavior occurs only at the impulsive control moment,the switching behavior in this paper is a characteristic of the complex network itself,which can occur at any moment after the initial moment of the network. |
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