Robustness of Hopfield Neural Networks Described by Differential Algebraic Systems of Index-1 under the Conditions of Deviation Argument and Stochastic Disturbance

Qing Liu,Ping Li,Zhibing Liu,Zuqiao Yang,Mehmet Emir Koksal

doi:10.1155/2021/1829466

Abstract

Robustness refers to the ability of a system to maintain its original state under a continuous disturbance conditions. The deviation argument (DA) and stochastic disturbances (SDs) are enough to disrupt a system and keep it off course. Therefore, it is of great significance to explore the interval length of the deviation function and the intensity of noise to make a system remain exponentially stable. In this paper, the robust stability of Hopfield neural network (VPHNN) models based on differential algebraic systems (DAS) is studied for the first time. By using integral inequalities, expectation inequalities, and the basic control theory method, the upper bound of the interval of the deviation function and the noise intensity are found, and the system is guaranteed to remain exponentially stable under these disturbances. It is shown that as long as the deviation and disturbance of a system are within a certain range, there will be no unstable consequences. Finally, several simulation examples are used to verify the effectiveness of the approach and are described below.

Highlights

Life is full of nonlinear phenomena, for example, the resistance of a plane and the starting of a car
Scholars have never stopped the comprehensive analysis of nonlinear systems and have mainly focused on system control, for example, adaptive neural finite-time stabilization [1], adaptive control [2, 3], repetitive control [4], output feedback stabilization [5, 6], system commutativity issues [7], H∞ control [8], and fuzzy second-order-like sliding mode control [9]
Systems with deviation argument (DA) are usually composed of differential equations and difference equations

Summary

Introduction

Life is full of nonlinear phenomena, for example, the resistance of a plane and the starting of a car. An adaptive neural network statefeedback controller was designed by building an appropriate Lyapunov function in [18]. Ere are other conclusions about the systematic control design of SD systems in references [19, 20] Extending these approaches to DASs is a challenging topic. The Lyapunov stability theorem, controller design, semigroup theorem, and linear matrix inequality (LIM) methods have difficulties achieving robustness for nonlinear systems with disturbances. Erefore, the interval length of a deviation and the quantitative index of the disturbance intensity are of great significance for the study of nonlinear systems. The robustness of index-1 DASs is studied by using the theory of parallel differential systems.

Preliminaries and Model Description

Properties

System Description