Partial Variable Stability for a Class of Nonlinear Systems with Time Delay

Ran Huo,Xiaoli Wang

doi:10.4236/am.2020.115027

Abstract

This article first gives a new class of integral inequalities. Then, as an application, the nonlinear neutral differential system with multiple delays is considered, and the trivial solution of the nonlinear neutral system with multiple delays is obtained. Uniform asymptotic Lipschitz stability. Obviously, the above system is a generalization of the traditional differential system. The purpose of this paper is to study the dual stability of neutral differential equations with delays, including equal asymptotically Lipschitz stability and uniformly asymptotic Lipschitz stability. The author uses the method of integral inequality to establish a double stability criterion. As a result, the local stability of differential equations is widely used in theory and practice, such as dynamic systems and control systems.

Highlights

In 1892, Lyapunov, a Russian mathematician, mechanician and physicist, proposed the notion of the stability of motion
The purpose of this paper is to study the dual stability of neutral differential equations with delays, including equal asymptotically Lipschitz stability and uniformly asymptotic Lipschitz stability
The author uses the method of integral inequality to establish a double stability criterion

Summary

Introduction

In 1892, Lyapunov, a Russian mathematician, mechanician and physicist, proposed the notion of the stability of motion He gave the general research methods in his doctoral dissertation “The general problem of the stability of motion” [1], in which he established the foundation of the stability theory. As a result, studying the partial stability of differential equations becomes more important. It is of practical significance to study the partial stability of differential equations. In 2002, Wang Feng used the differential inequality of delay in article [7] to study the following delay system:. In this paper the author consider a new class of the nonlinearly perturbed differential systems with time-delay ( ) dy. The author uses the method of differential inequalities with time-delay and integral inequalities to establish double stability criteria

Preliminaries

Main Results

Conclusion