Robust Performance Analysis And Synchonization Control For Neural Networks

Neural networks(NNs)have been extensively applied in image processing,pattern recognition,secure communication,optimization combination,and other engineering areas,which have attracted an increasing great interest amongst control community,mathematical community and etc,and many research results have been achieved.Based on the augmented Lyapunov functional and integral inequality methods,the robust performance analysis and synchronization control problems of neural networks are investigated.The research contents are outlined as follows,(1)The delay-dependent stability of neural networks with timevarying delay is discussed.A suitable augmented Lyapunov functional is firstly constructed,in which the information on the time-delay,time-delay state and activation function is taken fully into account.By employing the integral inequalities presented recently to estimate the derivative of Lyapunov functional,especially the free-matrix-based integral inequality is utilized to bound integral term without combining reciprocally convex technique and to avoid the conservativeness yielded form reciprocally convex.Then,the robust delay-dependent stability condition is obtained.Finally,numerical examples are given to illustrate the superiority of the proposed approach over the existing ones.(2)The robust delay-dependent dissipativity of a class of neural networks with time-varying delay is investigated.A proper augmented Lyapunov functional with triple integral items is constructed,in which some useful information ignored in existing literature is taken fully into account in the augmented vector of functional.By introducing two zerovalue equalities to further reduce conservatism in the deriving process,some delay-dependent dissipativity conditions for delayed neural networks,formulate in linear matrix inequality(LMI),are established,in which the relationship between the time-delay d(t)and its distance to the upper bound h-d(t)is fully considered by applying the free-matrix-basedintegral inequality,Writinger’s inequality and the combining reciprocally convex approach,meanwhile,the obtained results are extended to passivity analysis and some less conservative sufficient conditions are achieved to ensure the passivity of the considered neural networks.numerical examples are provided to show the effectiveness of the proposed method.(3)The problem of local synchronization of chaotic neural networks with actuator saturation is discussed.Considering limitations that the existing free-matrix-based integral inequality cannot be applied to sampled-data systems,two improved free-matrix-based inequalities are proposed.A time-dependent discontinuous Lyapunov function is established based on the improved free-matrix-based inequality,which takes advantage of the characteristic information of the actual sampling model.By employing sampled-data control method,a less conservative local stability criteria is obtained for synchronization error systems.Based on this criteria,the design method of the desired sampled-data controller is also given to ensure that the master system and slave system are locally asymptotically synchronous.(4)The exponential synchronization problem of neural networks with discrete and distributed delays is investigated.Based on a time-dependent continuous Lyapunov functional and discontinuous Lyapunov functional,respectively,some new synchronization criteria are established to guarantee that the master system is synchronous with the slave system,and the design method of the sampled-data controller is also given.Simulation example illustrate that the resulting criteria based on the discontinuous Lyapunov functional is more effective in reducing conservativeness than those based on the continuous Lyapunov functional.Finally,the research of stability,dissipativity and synchronization control for neural networks are summarized.In addition,the difficulties existing in the application and the direction of future studies are mentioned.