一类混合系统不变集的LMI方法求解-豆柴文库

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一类混合系统不变集的LMI方法求解
Title:LMI-BasedMethodsforSolvingInvariantSetsofaClassofHybridSystems
Abstract:
Inhybridsystems,whichconsistofbothcontinuousanddiscretedynamics,determiningthesetofstatesthatremainsinvariantduringthesystem'sevolutionisofgreatimportanceforstabilityanalysisandcontrolsynthesis.ThispaperfocusesonaclassofhybridsystemsandpresentsanoverviewoftheLMI-basedmethodsusedtosolvefortheinvariantsets.
1.Introduction(150words)
Hybridsystemshavegainedsignificantattentionduetotheirwiderangeofapplicationsinvariousfields,suchasrobotics,powersystems,andautomotivecontrol.Thesesystemsexhibitbothcontinuousdynamics,describedbydifferentialequations,anddiscretedynamics,representedbyswitchingmodes.Determiningtheinvariantsetsofthesesystemsiscrucialfordesigningrobustcontrollersandensuringsystemstability.Thispaperaimstoprovideanin-depthunderstandingoftheLMI-basedmethodsutilizedforsolvingtheinvariantsetsofaspecificclassofhybridsystems.
2.BackgroundonHybridSystems(200words)
Thissectionprovidesabriefoverviewofhybridsystems,includingtheirmathematicalrepresentation,modeswitchingbehavior,andkeypropertiesthatmakethemchallengingtoanalyze.Thedifferenttypesofhybridsystems,suchasimpulsive,switched,andpiecewise-affinesystems,arebrieflyintroduced,withanemphasisontheclassofhybridsystemsconsideredinthispaper.
3.ProblemFormulation(250words)
Inthissection,theproblemoffindingtheinvariantsetsofaclassofhybridsystemsisformallydefined.Theunderlyingassumptionsandsystemconstraintsareoutlined.Themathematicalformulationoftheproblem,expressedintermsoflinearmatrixinequalities(LMIs),ispresented.ThemotivationbehindusingLMIsisdiscussed,highlightingtheirabilitytohandlesystemconstraintsefficientlyandproviderobustsolutions.
4.LMI-BasedApproaches(400words)
ThissectiondescribesvariousLMI-basedapproachesproposedintheliteraturetosolvetheproblemoffindingtheinvariantsetsofhybridsystems.Themethodsarecategorizedintothreemajorgroups:quadraticLyapunovfunctions,linearLyapunovfunctions,andthesumofsquares(SOS)decompositionapproa