Stability Analysis Of Delayed Complex-valued Neural Networks With Discontinuous Activation Functions

After decades of development,neural network theory has gradually developed and matured,and has been widely used in practical problems such as pattern recognition,signal processing,associative memory and so on.The application of neural network in these problems is inseparable from the study of its dynamic properties,especially its stability.Complex-valued neural network is an extension of real-valued neural network,its state,connection weight and activation function are complex,and can solve some problems that can not be solved by real-valued neural network.At the same time,according to Liouville's theorem,the activation functions commonly used in real-valued neural networks can not be used in complex-valued neural networks.Thus it can be seen that the selection of activation function is very important to the dynamic properties of complex-valued neural networks.In this paper,the global exponential stability and robustness of complex-valued neural networks with discontinuous activation functions are studied by means of Filippov differential inclusion theory and Lyapunov-Krasovskii functional.As a generalization of real-valued neural network in complex domain,more stringent assumptions are needed to meet the stability of complex-valued neural network.In this paper,the complex-valued neural network is divided into real part and imaginary part,and then transformed into an equivalent real-valued neural network model,and its stability and robustness conditions are studied.Firstly,we study the global exponential stability of complex-valued neural networks with binary discontinuous activation functions.By using Lyapunov function,Filippov differential inclusion theory and Leray-Schauder alternative theorem,a sufficient condition for ensuring the global exponential stability of neural networks is obtained.Finally,a numerical simulation example is given to verify the validity of the conclusion.Secondly,we study the global robust exponential stability of a class of complex-valued neural networks with binary discontinuous activation functions.After similar treatment of complex-valued neural networks,sufficient conditions for global robust exponential stability of complex-valued neural networks are obtained by constructing new Lyapunov-Krasovskii Functionals,combining Kakutani fixed point theorem and Schur complement theorem.