Fractional-Order Vectorial Halanay-Type Inequalities With Applications for Stability and Synchronization Analyses

Peng Liu; Jun Wang; Zhigang Zeng

doi:10.1109/TSMC.2022.3201076

Fractional-Order Vectorial Halanay-Type Inequalities With Applications for Stability and Synchronization Analyses

Peng Liu, Jun Wang^*, Zhigang Zeng

^*Corresponding author for this work

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

21 Citations (Scopus)

Abstract

The Halanay inequality is widely used in various time-delayed dynamical systems analyses and its vectorial form has become available recently. In this article, the integer-order vectorial Halanay-type inequality is further extended to fractional-order ones in both time-invariant and time-varying forms. It is shown that the fractional-order vectorial Halanay-type inequalities hold under the derived conditions in the form of M-matrices. In addition, the time-invariant inequalities are applied to analyzing the stability and synchronization of fractional-order systems with two numerical examples to substantiate the theoretical results. © 2022 IEEE.

Original language	English
Pages (from-to)	1573-1583
Number of pages	11
Journal	IEEE Transactions on Systems, Man, and Cybernetics: Systems
Volume	53
Issue number	3
Online published	8 Sept 2022
DOIs	https://doi.org/10.1109/TSMC.2022.3201076
Publication status	Published - Mar 2023

Funding

This work was supported in part by the Key Project of Science and Technology Innovation 2030 through the Ministry of Science and Technology of China under Grant 2018AAA0100300; in part by the Research Grants Council of the Hong Kong Special Administrative Region of China under the General Research Fund under Grant 11202318, Grant 11202019, and Grant 11203721; in part by the 111 Project on Computational Intelligence and Intelligent Control under Grant B18024; and in part by the National Natural Science Foundation of China under Grant 62076222.

Research Keywords

Delay effects
Delays
Differential equations
Fractional-order systems (FoSs)
Indexes
Numerical stability
stability
Stability criteria
synchronization
time delay
vectorial Halanay-type inequality

RGC Funding Information

RGC-funded

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10.1109/TSMC.2022.3201076

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Cite this

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title = "Fractional-Order Vectorial Halanay-Type Inequalities With Applications for Stability and Synchronization Analyses",

abstract = "The Halanay inequality is widely used in various time-delayed dynamical systems analyses and its vectorial form has become available recently. In this article, the integer-order vectorial Halanay-type inequality is further extended to fractional-order ones in both time-invariant and time-varying forms. It is shown that the fractional-order vectorial Halanay-type inequalities hold under the derived conditions in the form of M-matrices. In addition, the time-invariant inequalities are applied to analyzing the stability and synchronization of fractional-order systems with two numerical examples to substantiate the theoretical results. {\textcopyright} 2022 IEEE.",

keywords = "Delay effects, Delays, Differential equations, Fractional-order systems (FoSs), Indexes, Numerical stability, stability, Stability criteria, synchronization, time delay, vectorial Halanay-type inequality",

author = "Peng Liu and Jun Wang and Zhigang Zeng",

year = "2023",

month = mar,

doi = "10.1109/TSMC.2022.3201076",

language = "English",

volume = "53",

pages = "1573--1583",

journal = "IEEE Transactions on Systems, Man, and Cybernetics: Systems",

issn = "2168-2216",

publisher = "IEEE Advancing Technology for Humanity",

number = "3",

}

TY - JOUR

T1 - Fractional-Order Vectorial Halanay-Type Inequalities With Applications for Stability and Synchronization Analyses

AU - Liu, Peng

AU - Wang, Jun

AU - Zeng, Zhigang

PY - 2023/3

Y1 - 2023/3

N2 - The Halanay inequality is widely used in various time-delayed dynamical systems analyses and its vectorial form has become available recently. In this article, the integer-order vectorial Halanay-type inequality is further extended to fractional-order ones in both time-invariant and time-varying forms. It is shown that the fractional-order vectorial Halanay-type inequalities hold under the derived conditions in the form of M-matrices. In addition, the time-invariant inequalities are applied to analyzing the stability and synchronization of fractional-order systems with two numerical examples to substantiate the theoretical results. © 2022 IEEE.

AB - The Halanay inequality is widely used in various time-delayed dynamical systems analyses and its vectorial form has become available recently. In this article, the integer-order vectorial Halanay-type inequality is further extended to fractional-order ones in both time-invariant and time-varying forms. It is shown that the fractional-order vectorial Halanay-type inequalities hold under the derived conditions in the form of M-matrices. In addition, the time-invariant inequalities are applied to analyzing the stability and synchronization of fractional-order systems with two numerical examples to substantiate the theoretical results. © 2022 IEEE.

KW - Delay effects

KW - Delays

KW - Differential equations

KW - Fractional-order systems (FoSs)

KW - Indexes

KW - Numerical stability

KW - stability

KW - Stability criteria

KW - synchronization

KW - time delay

KW - vectorial Halanay-type inequality

UR - http://www.scopus.com/inward/record.url?scp=85137872611&partnerID=8YFLogxK

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85137872611&origin=recordpage

U2 - 10.1109/TSMC.2022.3201076

DO - 10.1109/TSMC.2022.3201076

M3 - RGC 21 - Publication in refereed journal

SN - 2168-2216

VL - 53

SP - 1573

EP - 1583

JO - IEEE Transactions on Systems, Man, and Cybernetics: Systems

JF - IEEE Transactions on Systems, Man, and Cybernetics: Systems

IS - 3

ER -

Fractional-Order Vectorial Halanay-Type Inequalities With Applications for Stability and Synchronization Analyses

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GRF: Intelligent Mission Planning and Tracking Control of Autonomous Surface Vehicles Based on Neural Computation

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Fractional-Order Vectorial Halanay-Type Inequalities With Applications for Stability and Synchronization Analyses

Abstract

Funding

Research Keywords

RGC Funding Information

Access Output

Other Access Options

Permanent Link

Other Files and Links

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GRF: Neurodynamics-driven Optimization and Control of Intelligent Heating, Ventilation and Air Conditioning Systems

GRF: Collaborative Neurodynamic Approaches to Portfolio Optimization

GRF: Intelligent Mission Planning and Tracking Control of Autonomous Surface Vehicles Based on Neural Computation

Cite this