Abstract
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.
Highlights
It is well known that neural networks have many applications in the area of signal processing, pattern recognition etc
Hopfield neural networks (HNNs) have been widely applicated in power system
The timevarying delay usually exists in the HNNs and it has a negative influence on system performance
Summary
It is well known that neural networks have many applications in the area of signal processing, pattern recognition etc. [8] constructed an augmented LKF with more information about delays for HNNs with time-varying delays, and analyze its stability by the free weight matrix method. Besides the two aspects mentioned above, how to find the condition that guarantees the negative definiteness of the derivative of LKFs is important, especially when the derivative is a quadratic function with respect to the time-varying delay. A suitable LKF is constructed based on the delay and quadratic multiplication LKF, and the derivative of the LKF is estimated by the integral inequality method and a relaxed quadratic function negative-determination lemma is employed to obtain the asymptotic stability criteria of HNNs. a numerical example is given to demonstrate the advantages and effectiveness of the proposed method. State trajectories of the system of Example 1 Траектории состояний системы примера 1
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