Research On Analysis And Synchronization Control For Several Types Of Delayed Complex-valued Neural Networks Models

Recently,the research for complex-valued neural networks has been always a rapidly growing issue owing to complex-valued signals'extensive applications in many engineering areas.As a complex nonlinear dynamical system,the broad applications of neural networks rely heavily on its dynamical behaviors.Moreover,time delay is always unavoidable in practical systems and it is the main factor causing system deterioration.As a result,the dynamic behavior analysis of delayed complex-valued neural network systems has been widely concerned.Based on the current research results,by utilizing Lyapunov functional method,fixed time stability theory,Lyapunov stability theory,differential inclusion theory,M-matrix approach,homeomorphism property,and various inequalities,the delicate research of analysis and synchronization control problems for several kinds of delayed complex-valued neural network systems is presented.The main results of this thesis are shown as follows:1.The problems of Lagrange exponential stability and fix-time synchronization of complex-valued bi-directional associative memory(BAM)neural networks are studied.First,for complex-valued BAM neural networks with time-varying delays,on the basis of activation functions satisfying different assumption conditions,by combining the Lyapunov function approach with some inequalities techniques,different sufficient criteria including algebraic conditions and the condition in terms of linear matrix inequality(LMI)are derived to guarantee Lagrange exponential stability of the addressed system for the first time,respectively.Next,for complex-valued BAM neural networks with constant delay,based on the fixed-time stability,a new fixed time synchronization criterion is firstly presented,and a more accurate estimation independent on the initial conditions is given for the settling time compared with the existing results.Meanwhile,a new nonlinear delayed controller different from the existing ones is designed.2.The problems of exponential stability and exponential input-to-state stability of delayed complex-valued memristor-based BAM neural networks are studied.First,for complex-valued memristor-based BAM neural networks with constant delays,the assumptions of the complex-valued activation functions are relaxed.Via the differential inclusion theory,the equivalent real-valued system is obtained by separating the addressed system into real and imaginary parts.Then by utilizing Lyapunov stability theory,M-matrix approach and homeomorphism property,a sufficient criterion for the existence,uniqueness,and exponential stability for the equilibrium point of the considered system is derived for the first time.Next,for complex-valued memristor-based BAM neural networks with multiple time-varying delays,based on the same approaches,the equivalent real-valued system is obtained.By combining the Lyapunov function approach with some new inequalities techniques,a sufficient criterion of the exponential input-to-state stability is firstly derived.3.The state estimation problem of complex-valued memristor-based neural networks with time-varying delays is investigated.First,by combining the differential inclusion theory and separating the addressed system into real and imaginary parts,the equivalent real-valued system is obtained.Then,by utilizing the Lyapunov stability theory and some matrix inequality techniques,a sufficient delay-dependent condition which guarantees that the error-state system is global asymptotically stable is firstly presented,and an available state estimator is also designed.