Practical stability for fractional impulsive control systems with noninstantaneous impulses on networks

Jin You,Shurong Sun

doi:10.15388/namc.2022.27.25204

Abstract

This paper investigates practical stability for a class of fractional-order impulsive control coupled systems with noninstantaneous impulses on networks. Using graph theory and Lyapunov method, new criteria for practical stability, uniform practical stability as well as practical asymptotic stability are established. In this paper, we extend graph theory to fractional-order system via piecewise Lyapunov-like functions in each vertex system to construct global Lyapunov-like functions. Our results are generalization of some known results of practical stability in the literature and provide a new method of impulsive control law for impulsive control systems with noninstantaneous impulses. Examples are given to illustrate the effectiveness of our results

Highlights

Impulsive control has wide applications in real world
Some useful impulsive control approaches have been presented in many fields such as in financial models, epidemic models, neural networks and so on [6, 7, 17, 19, 21, 25]
The purpose of this paper is to study the practical stability for a class of impulsive CSFDENs with noninstantaneous impulses

Summary

Introduction

Impulsive control has wide applications in real world. Some useful impulsive control approaches have been presented in many fields such as in financial models, epidemic models, neural networks and so on [6, 7, 17, 19, 21, 25]. There are few relevant researches about stability analysis for coupled systems of fractional-order differential equations on networks (CSFDENs). Li [15] studied stability of fractional-order impulsive coupled nonautonomous (FOIC) systems on networks using graph theory and Lyapunov method to get stability for a kind of FOIC systems. In 2017, Agarwal [2] investigated practical stability of nonlinear fractional differential equations with noninstantaneous impulses and presented a new definition of the derivative of a Lyapunov-like function; see literatures [2, 3, 9, 11, 20] for more details. It is the first time to consider fractional-order coupled systems with noninstantaneous impulses via graph theory.

Preliminaries

Examples

Conclusions