Generalized Halanay Inequalities with Applications to Generalized Exponential Stability and Boundedness of Time-Delay Systems

Dehao Ruan,Yue Liu

doi:10.1155/2019/6072481

Abstract

In this paper, a class of generalized Halanay inequalities is investigated. Under some assumptions, the generalized exponential stability and boundedness are discussed by means of integral inequalities. We do not require the boundedness of the time-varying delays and coefficients. In addition, our results improve some previous works. At last, three examples and simulations are given to illustrate the effectiveness of the main results.

Highlights

In recent years, dynamical systems have come to play a more and more important role in many areas such as physics, population dynamics, electrical engineering, medicine biology, ecology, economics, and other areas of science and engineering. e main reason for this is that it allows us to model some kinds of natural scientific, social scientific, and engineering problems appropriately
In many dynamical systems such as telecommunication systems and population dynamics systems, time delays are not avoidable; it is well known that the delay may cause oscillation and instability in systems
It is important to consider the influence of the time delays in the investigation of these systems. erefore, stability and boundedness of dynamical systems with time delays have been extensively studied by many authors

Summary

Introduction

Dynamical systems have come to play a more and more important role in many areas such as physics, population dynamics, electrical engineering, medicine biology, ecology, economics, and other areas of science and engineering. e main reason for this is that it allows us to model some kinds of natural scientific, social scientific, and engineering problems appropriately. Erefore, stability and boundedness of dynamical systems with time delays have been extensively studied by many authors (see, for instance, [4,5,6, 8,9,10,11,12,13,14,15, 17, 18, 20, 21]). Motivated by the aforementioned discussions, we study the above inequality and derive new generalized exponential stability and Mathematical Problems in Engineering boundedness conditions; the obtained results improve and generalize some existing works.

Main Results

Examples and Simulations

Conclusion