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Stabilization of third-order differential equation by delay distributed feedback control.

Alexander Domoshnitsky¹, Shirel Shemesh¹, Alexander Sitkin¹

¹Department of Mathematics, Ariel University, Ariel, Israel.

Journal of Inequalities and Applications

|March 7, 2019

Summary

This summary is machine-generated.

This study addresses the lack of research on third-order delay differential equations by proposing a new approach to analyze their exponential stability. New methods for stabilization using delay feedback control are also introduced.

Keywords:

Cauchy function Delay differential equations Exponential stability Stabilization W-transform

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Area of Science:

Mathematics
Control Theory
Dynamical Systems

Background:

Limited mathematical literature exists on the exponential stability of third-order delay differential equations.
Existing stability analysis methods may not be directly applicable to these specific types of equations.

Purpose of the Study:

To fill the gap in mathematical literature regarding the exponential stability of third-order delay differential equations.
To propose a novel approach for studying the stability of these equations.
To explore new possibilities for stabilization using delay feedback control.

Main Methods:

Development of a new analytical approach for stability analysis.
Application of delay feedback control strategies.
Theoretical investigation of stability criteria.

Main Results:

A framework for analyzing the exponential stability of third-order delay differential equations has been established.
The proposed approach provides new insights into the stability behavior of these systems.
New methods for stabilization via delay feedback have been identified.

Conclusions:

The study successfully addresses a significant gap in the mathematical understanding of third-order delay differential equations.
The proposed methods offer a foundation for future research in stability analysis and control design.
The findings pave the way for practical applications in systems requiring robust stability with delays.