| In recent years,the dynamic behaviors of complex networks have attracted the attention of many researchers,especially the passivity and output synchronization problems of complex dynamic networks.In the existing literatures,the non-derivative coupled network models are studied.In fact,in some real networks,different time derivative nodes may cause different changes in other nodes.Therefore,it is very important to investigate complex networks with derivative coupling.Moreover,in real life,many systems should be modeled on complex networks with multiple weights.Obviously,it is very meaningful to study the passivity and output synchronization of complex dynamic networks with multi-derivative coupling.On the other hand,complex networks usually do not achieve passivity and output synchronization through their own conditions,and some adaptive control strategies are needed to ensure their passivity and output synchronization.Furthermore,in the process of model receiving output synchronization,external disturbances is ubiquitous,and the research on H_∞ output synchronization problem is particularly important.To the best of our knowledge,the passivity and output synchronization of complex networks with multi-derivative coupling has not been studied.Therefore,two types of network models with multiple derivative couplings are investigated in this paper.On one hand,the problem of passivity for the proposed network models is analyzed by utilizing some inequality techniques and Lyapunov functional method,and several synchronization conditions for complex dynamical networks with multiple derivative couplings are given.Moreover,by employing adaptive state feedback control strategy,some sufficient conditions for guaranteeing passivity and synchronization of models are obtained.On the other hand,we also study the output synchronization and H_∞ output synchronization.Furthermore,a adaptive controller is designed to ensure the output synchronization and H_∞ output synchronization of these network models.Eventually,several examples are presented to demonstrate the effectiveness of the derived results. |
