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1、IEEETRANSACTIONSONAUTOMATICCONTROL,VOL.58,NO.1,JANUARY2013187[11]F.MazencandM.Malisoff,StrictLyapunovfunctionconstructionsthesystemdynamicsareexactlyknown.ThepresenceofuncertaintiesunderLaSalleconditionswithanapplicationtoLotka-Volterrasys-(parametricandnonparametric)andexogenousdisturbances,ho
2、wever,tems,IEEETrans.Autom.Control,vol.55,no.4,pp.841854,Apr.maketheproblemchallengingandmotivatethestatederivativeestima-2010.tionmethodforuncertainnonlinearsystemsdevelopedinthetechnical[12]A.Proud,M.Pachter,andJ.DAzzo,Closeformation?ightcon-trol,inProc.AIAAGuid.,Navigat.ControlConf.Exhib.,Po
3、rtland,note.OR,1999,pp.12311246.Themostcommonapproachtoestimatederivativesisbyusingnu-[13]C.RabbathandN.Léchevin,SafetyandReliabilityinCooperatingUn-mericaldifferentiationmethods.TheEulerbackwarddifferenceap-mannedAerialSystems.Singapore:WorldScienti?c,2010.proachisoneofthesimplestandthemostcom
4、monnumericalmethods[14]W.RenandR.Beard,Trajectorytrackingforunmannedairvehicleswithvelocityandheadingrateconstraints,IEEETrans.ControlSyst.todifferentiateasignal;however,thisadhocapproachyieldserroneousTech.,vol.12,no.5,pp.706716,Sep.2004.resultsinthepresenceofsensornoise.Thecentraldifferenceal
5、go-[15]T.ShimaandS.Rasmussen,UAVCooperativeDecisionandControl:rithmperformsbetterthanbackwarddifference;however,thecentralChallengesandPracticalApproaches.Philadelphia,PA:SIAM,differencealgorithmisnoncausalsinceitrequiresfuturestatevalues2009.toestimatethecurrentderivative.Noiseattenuationinnum
6、ericaldif-[16]E.D.Sontag,Input-to-statestability:Basicconceptsandresults,inNonlinearandOptimalControlTheory,P.NistriandG.Stefani,Eds.ferentiatorsmaybeachievedbyusingalow-pass?lter,atthecostBerlin,Germany:Springer,2008,vol.1932,LectureNotesMath.,pp.ofintroducingaphasedelayinthesystem.Amoreanalyt
7、icallyrig-163220.orousapproachistocasttheproblemofstatederivativeestimationas[17]K.Valavanis,P.Oh,andL.Piegl,UnmannedAircraftSys-anobserverdesignproblembyaugmentingthestatewithitsderiva-tems.London,U.K.:Springer,2009.tive,wherethe
