A new criterion of asymptotic stability for Hopfield neural networks with time-varying delay

The objective of this paper is to analyze the stability of Hopfield neural networks with time-varying delay. For the system to operate in a steady state, it is important to guarantee the stability of Hopfield neural networks with time-varying delay. The Lyapunov-Krasovsky functional method is the main method for investigating the stability of time-delayed systems. On the basis of this method, the stability of Hopfield neural networks with time-varying delay is ana-lysed. It is known that due to such factors as communication time, limited switching speed of various active devices, time delays often arise in various technical systems, which significantly degrade the performance of the system, which can in turn lead to a complete loss of stability. In this regard, a Lyapunov-Krasovsky type delay-product functional was con-structed in the paper, which allows more information about the time delay and reduces the conservatism of the method. Then a generalized integral inequality based on the free matrix was used. A new criterion for asymptotic stability of Hop-field neural networks with time-varying delay, which has less conservatism, was formulated. The effectiveness of the proposed method is illustrated. Thus an asymptotic stability criterion for Hopfield neural networks with time-varying delay was formulated and justified. The expanded Lyapunov-Krasovsky functional is constructed on the basis of delay and quadratic multiplicative functional, and the derivative of the functional is defined by a matrix integral inequality with free weights. The effectiveness of the method is illustrated by a model example.

Multistability Analysis of State-Dependent Switched Hopfield Neural Networks With The Gaussian-Wavelet-Type Activation Function*

This paper studies the multistability of state-dependent switched Hopfield neural networks (SSHNNs) with the Gaussian-wavelet-type activation function. The coexistence and stability of multiple equilibria of SSHNNs are proved. By using Brouwer's fixed point theorem, it is obtained that the SSHNNs can have at least 7n or 6n equilibria under a specified set of conditions. By using the strictly diagonally dominance matrix (SDDM) theorem and Lyapunov stability theorem, 4n or 5n locally stable (LS) equilibria are obtained, respectively. Compared with the conventional Hopfield neural networks (HNNs) without state-dependent switching or SSHNNs with other kinds of activation functions, SSHNNs with this type of activation functions can have more LS equilibria, which implies that SSHNNs with Gaussian-wavelet-type activation functions can have even larger storage capacity and would be more dominant in associative memory application. Last, some simulation results are given to verify the correctness of the theoretical results.

Inequalities and pth moment exponential stability of impulsive delayed Hopfield neural networks

In this paper, the pth moment exponential stability for a class of impulsive delayed Hopfield neural networks is investigated. Some concise algebraic criteria are provided by a new method concerned with impulsive integral inequalities. Our discussion neither requires a complicated Lyapunov function nor the differentiability of the delay function. In addition, we also summarize a new result on the exponential stability of a class of impulsive integral inequalities. Finally, one example is given to illustrate the effectiveness of the obtained results.