Stability Analysis And State Observer Design Of Discrete-time Higher-order Cohen-Grossberg Neural Networks With Time-varying Delays

Neural network is a complex network system composed of a large number of simple neurons.Although its concept is generated independently,with the passage of time,it is naturally combined with other disciplines,and has shown very good application in many practical fields.Moreover,it is gradually found that compared with the ordinary low-order neural networks,the high-order neural networks have better performance.On the other hand,in the process of neuronal information transmission,time-delay is almost inevitable,so time-delay neural network has also received very extensive attention.In this article,the stability and state estimation of discrete-time high-order Cohen–Grossberg(C–G)neural networks with time-varying delays are studied.The main research contents are as follows:First,the global exponential stability of discrete-time high-order Cohen–Gross berg neural networks with time-varying delays is studied.In this article,the global exponential stability criteria are obtained directly based on the definition of global exponential stability,and the obtained stability criteria are actually to judge whether a matrix is a non-singular M-matrix,which is easy to verify,a pair of numerical examples demonstrate the effectiveness of the proposed method.Secondly,considering the influence of impulse phenomenon on stability,the global exponential stability of discrete-time high-order C–G neural networks with time-varying delays and impulses is studied.We construct a new impulse-free system,and based on a technical lemma,we find the correspondence between the solutions of the impulse-free system and the impulse-free system.By studying the global exponential stability of the impulse-free system,we derive the global exponential stability criterion of the impulse-free system.The stability criterion is also used to determine whether a matrix is a nonsingular M-matrix,a pair of numerical examples demonstrate the effectiveness of the proposed method.Then,considering the influence of bounded perturbations on the stability,the global exponential stability of discrete-time high-order C–G neural networks with time-varying delays and bounded perturbations is studied in the Lagrange sense.Based on the definition of global exponential stability in Lagrange sense,the stability criteria are given directly,and the matrix inequality in the stability criteria involve very few decision variables,which is easy to solve.Numerical examples demonstrate the effectiveness of the proposed method.Finally,the state estimation problem of discrete-time high-order neural networks with time-varying delays and bounded perturbations is studied.Based on the definition of global exponential stability,the global exponential stability criteria of the error system are derived,and the state observer is designed for the neural network by using the Moore–Penrose inverse of the matrix.Two numerical examples are given to illustrate the effectiveness of the proposed observer.The innovation of this article lies in:(1)Avoiding the construction of Lyapunov–Krasovskii(L–K)functional;(2)The established stability criterion is easy to be solved,and its conservatism is lower.Moreover,the method presented in this article can be applied to most discrete system models with impulses and time delays.