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New delay range–dependent stability criteria for interval time-varying delay systems via Wirtinger-based inequalities
journal contribution
posted on 2018-01-25, 00:00 authored by R Mohajerpoor, Lakshmanan Shanmugam, Hamid AbdiHamid Abdi, R Rakkiyappan, Saeid Nahavandi, P ShiStability conditions for time-delay systems using the Lyapunov-based methodologies are generically expressed in terms of linear matrix inequalities. However, due to assuming restrictive conditions in deriving the linear matrix inequalities, the established stability conditions can be strictly conservative. This paper attempts to relax this problem for linear systems with interval time-varying delays. A double-integral inequality is derived inspired by Wirtinger-based single-integral inequality. Using the advanced integral inequalities, the reciprocally convex combination techniques and necessary slack variables, together with extracting a condition for the positive definiteness of the Lyapunov functional, novel stability criteria, have been established for the system. The effectiveness of the criteria is evaluated via 2 numerical examples. The results indicate that more complex stability criteria not only improve the stability region but also bring computational expenses.
History
Journal
International journal of robust and nonlinear controlVolume
28Issue
2Pagination
661 - 677Publisher
WileyLocation
Chichester, Eng.Publisher DOI
ISSN
1049-8923eISSN
1099-1239Language
engPublication classification
C1 Refereed article in a scholarly journalCopyright notice
2017, John Wiley & Sons, Ltd.Usage metrics
Keywords
Science & TechnologyTechnologyPhysical SciencesAutomation & Control SystemsEngineering, Electrical & ElectronicMathematics, AppliedEngineeringMathematicsinterval time-varying delaylinear matrix inequalityLyapunov Krasovskii methodWirtinger-based integral inequalitiesLINEAR-SYSTEMSPARTITIONING APPROACHROBUST STABILITYSTABILIZATIONMechanical Engineering
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