简介：Inthispaper,theexponentialstabilityanalysisforODEswitchedsystemswithtimedelayisextendedtodistributedparameterswitchedsystems(DPSS)inHilbertspace.Foragivenfamilyofexponentialstablesubsystems,thispaperfocusesonfindingconditionstoguaranteetheoverallDPSS'exponentialstability.Basedonsemigrouptheory,byapplyingpiecewiseLyapunov-Krasovskiifunctionalsmethodincorporatedaveragedwelltimeapproach,sufficientconditionsforexponentialstabilityarederived.Theseconditionsaregivenintheformoflinearoperatorinequalities(LOIs)wherethedecisionvariablesareoperatorsinHilbertspace,andthestabilitypropertiesdependonswitchingrule.Beingappliedtoheatswitchedpropagationequations,theseLOIsarereducedtostandardLinearMatrixInequalities(LMIs).Finally,anumericalexampleisgiventoillustratetheeffectivenessoftheproposedresult.

简介：Thedynamicinput-outputsystemiswellknownineconomictheoryandpractice.Inthispapertheasymptoticstabilityandbalancedgrowthsolutionofthedynamicinput-outputsystemareconsidered.Underthreenaturalassumptions,weobtainfourtheoremsaboutasymptoticstabilityandbalancedgrowthsolutionofthedynamicinput-outputsystemandbringtogetherinaunifiedmannersomecontributionsscatteredintheliterature.

简介：Inthispaper,weinvestigatethepthmomentuniformlyasymptoticstabilityofimpulsivestochasticfunctionaldifferentialsystemsbyextendingsomeRazumikhin-typetheorems.BasedontheLyapunovfunctionsandRazumikhintechniques,somecriteriaareestablishedandtheirapplicationstoimpulsivestochasticdelaysystemsareproposed.Anillustrativeexampleshowstheeffectivenessofourresults.

简介：InthispapermethodsofdifferentialinequalitiesandLiapunovfunctionalsforprovingtheglobalstabilityofconstantequilibriaofreaction-diffusionsystemsaregiven,andexamplesforshowinghowtousethesemethodsarealsogiven.

简介：这份报纸为改变系统由延期建模的延期的交换非线性的时间的一个班处理稳定性问题微分方程。旁边在箭头形式下面并且用新构造Lyapunov功能转变系统表示，聚集技术，Borne-Gentina实际稳定性标准与性质联系了，考虑系统的新延期无关的稳定性条件被建立。与在这的存在结果相比区域，获得的结果是明确的，对使用简单并且允许我们避免寻找普通Lyapunov的问题功能。最后，一个例子被提供，与数字模拟，到表明建议方法的有效性。

简介：Thispaperfocusesonthestabilityanalysisoftheactivedisturbancerejectioncontrol(ADRC)foraclassofuncertainsystems.ToovercomethedifficultyofdefiningareasonableLyapunovfunctionandsettinglimitationsofsystemparameters,theconverseLyapunovtheoremandthedisturbancetheoryareemployed.Thispaperprovesthattheestimationerroroftheextendedstateobserver(ESO)andthetrackingerroroftheclosed-loopsystemusingADRCareuniformlyultimatelyboundedandmonotonouslydiminishingwiththeincreaseoftheirrespectivebandwidth,sothatthestabilityoftheADRCsystemcouldbeperformed.Inordertofurtherillustratetherelationshipbetweenthestabilityrangeandbandwidths,itanalyzesquantitativelytheperformanceofESOandADRCbasedontherootlocusandthestepresponse.Finally,anexamplebasedonatypicalcontrolsystemiscarriedout,andsimulationresultsverifythetheoreticalanalysisprovedinthispaper.

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简介：Theproblemsofrobuststabilityandrobuststabilitywithaguaranteeingcostfordiscretetime-delaysystemswithnonlinearperturbationarediscussed.AsufficientcriterionforrobuststabilityisestablishedinanLMIframeworkandalinearconvexoptimizationproblemwithLMIconstraintsforcomputingmaximalperturbationboundisproposed.Meanwhile,asufficientcriterionforrobuststabilitywithaguaranteeingcostforsuchsystemsisobtained,andanoptimalprocedurefordecreasingthevalueofguaranteeingcostisputforward.Twoexamplesareusedtoillustratetheefficiencyoftheresults.

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