The Passivity Of The Coupled Neural Network With Nodes Of Different Dimensions Is Synchronized With H_∞

Recently,a larger number of researchers have greatly focused on the dynamical behaviors of complex networks,which include stability,synchronization and passivity.However,the coupled neural networks considered in the existing works are composed of identical nodes,the problem of passivity for coupled neural networks with different dimensional nodes has not yet been investigated.Hence,the paper investigates the passivity and pinning passivity of coupled different dimensional neural networks respectively.In addition,to the best of our knowledge,the problem of H_∞synchronization for coupled neural networks with non-identical nodes has not been discussed before.For this purpose,we also investigate the H_∞synchronization problem of coupled neural networks with non-identical nodes of the same dimensions and different dimensions in this thesis.On the other hand,due to limitations of equipment and environmental noises,the precise values of parameters in the networks cannot be obtained in many real situations.Therefore,we investigate the robust H_∞synchronization of coupled neural networks with non-identical nodes.Furthermore,considering coupled neural networks could not realize H_∞synchronization through themselves in practical situations,we study the problems of pinning adaptive H_∞synchronization and robust pinning adaptive H_∞synchronization for coupled neural networks with non-identical nodes.In this thesis,we investigate the passivity and H_∞synchronization of coupled different dimensional neural networks by using Lyapunov stability theory,various inequality techniques,graph theory and so on.First,several output-strict passivity,input-strict passivity,passivity criteria are proposed for coupled different dimensional neural networks and coupled different dimensional delayed neural networks through constructing Lyapunov functional and making use of inequality techniques.Second,by designing appropriate pinning controllers,we study pinning passivity of coupled different dimensional neural networks,and coupled different dimensional delayed neural networks with fixed coupling strength and adaptive coupling strength respectively.Third,considering that the external perturbations have an effect on coupled neural networks with non-identical nodes,H_∞synchronization of coupled neural networks with and with-out parametric uncertainties are discussed,and some criteria are established for the considered networks to realize H_∞synchronization and robust H_∞synchronization.Finally,some examples are presented to verify the effectiveness of theoretical results.