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Stability analysis of fractional differential time-delay equations
journal contribution
posted on 2017-04-25, 00:00 authored by N T Thanh, Hieu TrinhHieu Trinh, V N PhatThis study provides a novel analytical approach to studying the solutions and stability of fractional differential delay equations without using Lyapunov function method. By applying the properties of Caputo fractional derivatives, the Laplace transform and the Mittag-Leffler function, the authors first provide an explicit formula and solution bounds for the solutions of linear fractional differential delay equations. Then, they prove new sufficient conditions for exponential boundedness, asymptotic stability and finite-time stability of such equations. The results are illustrated by numerical examples.
History
Journal
IET control theory & applicationsVolume
11Issue
7Pagination
1006 - 1015Publisher
Institution of Engineering and TechnologyLocation
Stevenage, Eng.Publisher DOI
ISSN
1751-8644eISSN
1751-8652Language
engPublication classification
C Journal article; C1 Refereed article in a scholarly journalCopyright notice
2017, The Institution of Engineering and TechnologyUsage metrics
Keywords
asymptotic stabilityLyapunov methodsdelaysLaplace transformsstability analysisexponential boundednessfractional differential time-delay equationsLaplace transformMittag-Leffler functionfinite-time stabilityCaputo fractional derivativesLyapunov function methodIntegral transformsDistributed parameter control systemsStability in control theoryScience & TechnologyTechnologyAutomation & Control SystemsEngineering, Electrical & ElectronicInstruments & InstrumentationEngineeringORDER SYSTEMSMechanical Engineering
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