14337.基于lmi的離散時滯系統(tǒng)的穩(wěn)定性分析

1、霸弋逆紗分類號UDC密級公開一Z翥廬夕擎碩士研究生學位論文基于LMI的離散時滯系統(tǒng)的穩(wěn)定性分析申請人：譚聚龍學號：2131060培養(yǎng)單位：數學科學學院學科專業(yè)：運籌學與控制論研究方向：時滯系統(tǒng)理論指導教師：呂建婷副教授副導師：高翔宇副教授完成日期：2016年5月20日黑龍江大學碩士學位論文AbstractItiswellknownthattimedelayisfrequentlyencounteredinmanyrealsystems，

2、itcanoftendestroyinstabilityandeveninfluenceonthesystemperformance，therefore，theresearchofstabilityproblemforthetimedelaysystemshastheimportanttheorysignificanceandthepracticaltimedelayinpracticesuchthatalotappof1ication

3、valueJustbecausethereexistsdifficultiesappearinstabilityanalysisofthetimedelaysystems，thus，thestabilityproblemofthetime—delaysystemshasbecomethefocusofcontroltheoryandapplicationThispapermainlystudiestwoproblems：Oneisthe

4、asymptoticallystableproblemofthediscretetimelinearsys—temwithconstanttimedelay，andtheotheristheasymptoticallystableproblemofthediscretetimelinearsystemwithtimevaryingdelaysFirstly，byintroducingadiscreteinnerproduct，aseto

5、fdiscreteorthogonalpolynomials(DOPs)isobtainedbyapplyingtheGram—SchmidtorthogonalizationprocessFromwhich，weproveaDOPs—basedsummationinequalitycontaininganonnegativeintegerN箍aparameterThelargertheparameterNis、themoreaccur

6、atetheDOPsbasedsummationinequalitybecomesThen，theDOPs—basedsummationinequalityisappliedtoestablishstabilitycriterionforaclassoflineardelayeddiscrete—timesystemsComparedwiththeLMI—basedstabilitycriteriainmostoftheliteratu

7、re，thestabilitycriteriainthischapterreducethecomputationalcomplexitygreatlyByconstructinganappropriateaugmentedLyapunovKrasovskiifunctional，adelaydependentstabilitycriterionintheformoflinearmatrixinequalityisobtainedMeth

8、odsproposedinliteratureisimproved，thatis，thedelayintervalisdividedintosmallrangetodealwithLyapunov—KrasovskiiThestabilitycriteriongiventohereiSlessconservativethantheexistingonesKeywords：Discreteorthogonalpolynomials；Lya