Samenvatting
We present a general emulation-based framework to address the distributed control of multi-Agent systems over packet-based networks. We consider the setup where information is only transmitted at (non-uniform) sampling times and where packets are received with unknown delays. We design local dynamic periodic event-Triggering mechanisms to generate the transmissions. The triggering mechanisms can run on non-synchronized digital platforms, i.e., we ensure that the conditions must only be verified at asynchronous sampling times, which may differ for each platform. Different stability and performance characteristics can be considered as we follow a general dissipativity-based approach. Moreover, Zeno-free properties are guaranteed by design. The results are illustrated on a consensus problem.
| Originele taal-2 | Engels |
|---|---|
| Pagina's (van-tot) | 168-173 |
| Aantal pagina's | 6 |
| Tijdschrift | IFAC-PapersOnLine |
| Volume | 55 |
| Nummer van het tijdschrift | 13 |
| DOI's | |
| Status | Gepubliceerd - 2022 |
| Evenement | 9th IFAC Conference on Networked Systems, NECSYS 2022 - Zurich, Zwitserland Duur: 5 jul. 2022 → 7 jul. 2022 Congresnummer: 9 |
Bibliografische nota
Funding Information:einstsoenatciacolutnot,teaskpeectihaellysawmhpelninfgastbesahmavpiolirngofistnhoetpploastsfiobrlme, counatrraanctteiev)i.tyA, pno∈ta[1b,le∞a)d,viasnotfaigneteorfeosturasseatusptriisngthsattabcliolictky ecinsotsnoednaccouittiiaolnstnoat,rteespakoefecitettnhhaleeplyrsoaawhmceppsenslliienndfggastobnesampahadviigoliirntagolfipstlnahottefoppprllmossiaat,foibtrlme,is claournatrcraaanscette)ieva)i.tndyA,pnveo∈hicta[1ble,le∞-plaa)d,vtoiasnootnfaingigneteoprorfeostubrlemasseatsusp(intriisnwgthhsaitctahbcliLolictpky-ien.gto. ainccocausnet,oefspleocwia-plloywwehreenlefcatsrtosnaimcsp,lingwishnicohtpcoassseibwlee, syunacrhanrotneeiz)a.tAionoitsanboletaredqvuainrteadg.eHoefnocueresaecthuploicsatlhpalattcflorcmk e.g. in case of low-power electronics, in which case we gyounatcrrhaanrcottneieviz)ia.tytA,iopno∈itsa[1nb,ole∞t ar)ed,qviuasinortefadig.netHeoerfneosctueraesaecathuspltoricisnagtlhpsaltatatbcfliolrictmky eta.glk. ionf pcearsieodoifc leovwen-pt-otwriegrgeerleedctcroonnticrso,l,isneew, he.igch., Hcaeseemweles syancsharmonpilzeatainond itsrannostmreitquinirdeedp.eHnednecnetleyacohf alollcaolthpelartpfolramt-eetna..ggtlko.. aiioncfcpocceaaurssnieeot,doeifcspleeovcwweina--ppltl-oytwrwieeghrrgeeeenrlleeefdccattscrtosnatimccrssop,,l,linsnegewi,shen.igcoh.t, pHccoaaessseseemibweleles, syaunacrshaanrmotnepeilz)ea. tAainondoittsraanbnolestmareditqvuaininrdteaedpg.eeHnoedfneocnuetrleysaecothfuaplollicsaotlthpaelatrtcpfloloracmtk-teatlkalo. f(p20er1i3o)d.icMeovreenotv-etrr,igignerpedraccotincter,olt,hseeec,oem.gm.,uHnieceamtieolns foarnmsa, mpalkeinagndthteraanlgsmoriitthinmdefuplelnyddeinsttlryiboufteadll. other plat-ee.tg.ali.n(2c0a1s3e).ofMloowre-opvoewr,erinelpercatcrotinciec,s,the communicatiwone coarnmsa,mpalkeinagndthteraanlgsmoriitthinmdefuplelnyddeinsttlryiboufteadll. other plat-nanetdwuornkknsouwffnersdeflraoyms, iwmhpicehrfemctaiyondsesutrcohy asstatbimiliety-vaorfytinhge 2. PRELIMINARIES neteetawlo. r(k20s1uu3ffff)e.rsMforroemoveiimmr,pienrrffpeecrttaiicootnicsse,sutchhe acsomttiimmmuee-nvviacraytiionng forms, making the2.algPoRErithmLIMfullyINARIEdistribS uted. closed-loop system. While there is abundant literature on For space reasons,2.somePRELIMprelINARIEiminariesS are omitted. An teh.ge.,eNveonwtz-tarriggeteraeld. (c2o0n1t9ro)lanofdmreufeltrie-nagceesntthseyrsetienm, st,ostehee, FFxootrrenspsdpeaceadceverresaiosonnos,f tshoims peappreerliimncilnuadriinesg aalrlenootmatitiotends.thAant tceh.lgoe.s,eeedNvv-eeolonnwottz--pttarrsiiyggsggetteeerrmaeeldd. W(cc2oo0hnn1itl9reoo)tllahnooeffrdemriesufealltrbiie--unaanggcdeeesannntttthsselyyirtsseettirenamm,tusst,,oressteeoheene,, eb.egs.t, oNfoowuzrakrni oewt laeld.g(e2,0n1o9n)eaonfdthreefperroenpcoessedthaeprperinoa, cthoesthine extended version of this paper including all notations that btthh.eestgees.t,leioofNNtvfeeooroounwwauttzz-rrutaakkrrrreinngoocgewwoternllaeeedslddi..dgge,e(ec2r,o0nnna1toonl9lrno)oeelfaaoofnnotfhfdttehhmrreefeeouffppleelltrrrroioope-wpnaigccoosedneeesgssendtatshaapspepyerppsectrritenoosmaa:, ccstthh,oesesstehiienne, beth.eegess.tt,liooNtffeoroowauutzrruakrrenni ocewwotnllaeeslddi.dgge(ee2r,,0nna1ol9ln)oeefaoontffhdttehhrefeofplelroooewpnpicoonessgseeddatshaapepperpecritnoosaa:, ccthoesthiine arxroetreunsseddpeeaddcecanvaernresabioseonnfouosu,fntshdoimsonnpeaarpprreXierilviimn,ciseelneuaedrSinecsgheraarlreslesnetoottmaaltilti.ote(nd2022)s0.t2hA2a)nt. the(1)litenoranlineturearcmonsulideti-srysaltelmofstehtup,e following aspects: arxreeteuncseddoeneddsicandvaenrrsbihoeynfbourufidnthdsisyonsnptaearpmreXisrivion,fcseeletuhedeSincfghoerramrleslsnHetott(aCalt,li.oF(n,2022)sD0t2,h2Ga))t. tbheestliotferoautrukrenocwonlesdidgeer, naollnoefotfhtehefooplllroowpionsgedasappeepccrttossa:: ches in We consider hybrid systems of the form H(C, F, D,G) (12)) nfuolnlylindeisatrrimbuutlteid-saynstdemasysentcuhpro, nous configuration, given by ξ = F(ξ,v), when ξ ∈ C ⊆ X, and ξ ∈ G(ξ), the(12))litennfuoolrannlylliiturenndeeisaatrrcimobnsuuutllidtteiid--esrayynalssttdleemaofsystenhttceuuhppfrolo,,nolowusincgonfigaspecturas:tion, Wgivee ncobynsidedξ˙e=r hFy(bξr,ivd),syswhteenmsξ o∈fnvCthe⊆ foX,rmandHξ(C++,F,∈ DG,G(ξ),) (23)) fimulplyledmisetnrtibabuitleitdyaonnddaisgyitnaclhprolantofoursmcso,nfiguration, gwihven ξby∈ξD=⊆F(Xξ,,vw)h,ewrehevn∈ξ L∈nC i⊆s aXn,eaxnodgeξnou∈s iGn(pξu)t, ((223))) ffimuullnlinepllyyleddmiissaettnrrrtiimbbabuuuittllteeiitd-ysaysonnntedddmaisgyysitennatup,cclhhprroolanntoofouurssmccsoo,nnffiigguration, Wgwhiveeenncoξbyns∈idξ˙˙De=r ⊆hFy(Xbξr,,ivdwh),seryswheteevnmnξ∈sξ Lo∈f∞vvCthi⊆se anfoX,rmexanogendHξ(C+ou, F,∈s DiGn,G(puξ),t) (34)) iumnpknleomwentanbdilittyimoen-vdairgyitinagl pslaamtfoprlimngs, and transmis-(wdhisetnurξba∈ncDe)⊆anXd, Xwh⊆ereRv ∈wLit∞h nisξ a∈n Nex>o0g,esneoeusGionepbuetl ((334))) ifullyumnppknlleeodismwentributetaanbbdiilliittdtyimaonden-vddaaiirsggyyniittinaacgllhprsolaanomtfousprlimncgso,nfiganduratrationsn,mis-g(whdihviseentnurξbbya∈nξ˙cDe=)⊆Fan(Xdξ,,Xvwh)h,⊆erwrehRevnnξξ∈ξwL∈itn∞hvCni⊆sξan∈Xn,Neax>no0dg,eξsn+eoueu∈sGiGone(pubξue)tl, (4) usinoknndoewlanysa,nd time-varying sampling and transmis-(edtiastl.ur(b2a0n12ce))aannddHXeem⊆elRsnetξ wali.t∞nh(v2n02ξ1∈).NFo>r0,thseeeseGhyobebrield (3) ismiopnledmeleanytsa,bility on digital platforms, (wdhisetnurξba∈ncDe)⊆anXd, Xwh⊆ereRv ∈wLith nis a∈n Nexog,esneoeusGionepbuetl (5) sgieonnerdaellastyasb,ilityandperformancepropertiesfor(pos-sytsatel.m(s2,01w2e)aarnediHnteeermesetlesdneξξtinalt.h(e20fo2l1l)o.wFinogrtdhiesssiepahtyibvritidy (45)) sgienoonknnenrdoaeewlllasntyasab,nidlitytimaned-vpaerryfionrgmsaanmcepplirnogpearntdiestrfoarns(mpoiss-(sdytsiasttel.umr(bs2,a0n1w2ce))aranenddiHnXteeerm⊆esetlResdetinwalit.thh(e2n0fo2l1l∈)o.wNFinogr ,tdhsiesesseiepGahtyoibevbritiedyl (5) gsiebnleyraulnsbtoaubnilditeyd)anadttpraecrftoorrms(aansceinprcopnesertniseussf)o.r(pos-syrsotpeemrtsy,,wehiacrheisinctleorseestiendniantutrheetofotllhoewoinngeduissesdipiantiTvieteyl (5) gsiieobnnnleeyrdauelnlasbttyoaasubb,niilldiitteyd)aanadttpraeecrrfftooorrmms(aaannscceeinprcoopneserrttniiseeusssf)o.r(pos-sytrsoatpel.emr(ts2y,0,1ww2eh)iacrhnedisiHncteleoersmeesetilensdentiantault.rhe(e2t0ofo2tl1lh)oe.wFoinongretduhisesesdiepiahntyiTbvrietiedyl Manysiblyworkusnbtroeatundead)subasetttraofctotrshese(asaspinectconss.eAnspusromi). nent p2r0o1p0e)r.ty, which is close in nature to the one used in Teel (5) siebnleyraulnsbtoaubnilditeyd)anadttpraecrftoorrms(aansceinprcoopnesertniseussf)o.r(pos- (p2010)yrsotpeemr.tsy,, wehiacrheisinctleorseestiendniantutrheetofotllhoewoinnge duissesdipiantiTvieteyl MMexaaannmyypwwleooirrskk,sse.ttgrr.eeat,atthaaessuruecbbessetnet oofwfottrhhkeesebseyaaspYsupeectacntss.d.CAAhppenrroomi(m2i0nn2ee1nn)tt, (Defini2010)ti.on 1. Let s : X×Rnnv → R be a supply rate and sibly unbounded) attractors (as in consensus). p2r0o1p0e)r.ty, which is close in navture to the one used in Teel Mewxhaainmcyhpwlperoooirrsvk,isdee.tgrs.eat,imthpaeosurrteacbnesetnttadofwvoatrnhkcesebemyaspeYnutsectaonns.dtCAhhepennromio(n2l0inn2ee1na)tr, S(2010)e⊆finiXt.iobne1a. cLleotsesd:nXon×-eRmnpvty→seRt. bSeysatesmupHplyisrastaeidantdo eMwxxhaaainmmcyhppwllperooirssvk,,isdee.tgrs.e,,iamtthpaeeosrrruteeaccbneesnntetadowwfvooatrrnhkkcebesemyyaeYsnuptseacontnsdd.tCAhhepeennro(mn22li00inn22ee11na))tr,, SDefini⊆ Xtionbe1.a cLetloseds :nXon×-empR ty→setR. beSystaemsupplHyisrastaeidantod wcahsiechwiptrhov(liadregsei)mupnokrntaonwtnatdrvaannscmeimsseinotnsdoenlatyhsewnhoinlelintaeakr-bSe⊆s-fXlowb-ediassicplaostievdenwointh-ermenspvptyectsetto.Sy,sotreminsHhoirst,s(asid,St)o-case with (large) unknown transmission delays while tak-bSDee⊆fsin-fiXltoiwobn-ed1ias.sicLpleaotstievsde:nwXoint×h-erRmespptye→ctsetRto. bSey, soatresmiunpsHphlyoirsrta,st(aesid,aSnt)do-case with (large) unknown transmission delays while tak-fbloews--dflioswsi-pdaitsisviep,atifivtehewriethexriesstps eactlotcoalSly, oLripinschshitozrtf,un(sc,tSio)n-⋆cahsiechwiptrhov(liadregsei)mupnokrntaonwtnatdrvaannscmeimsseinotns doenlatyhsewnhoinlelintaeakr-fbSloew⊆s-dfXlioswsbi-pedaiatsisvicepl,aostifievdtehnewroienth-eexrmiessptpstyeactsloettco.alSlyy, soLtreipminschsHhitozirstf,usn(asicd,tSiot)no-⋆ This work is supported by the ANR grant HANDY 18-CE40-0010. flow: X-d→issiRpa⩾t0i,vec,ailfletdhearesteoxraisgtes faulnocctaiollny,Lsuipcshchtihtaztfunction ⋆caThisse wwithork(lais suprgep)ortedunknboywthen traANnsR gmraisnstioHnANdeDlYay18s-CEwhile40-0010.tak- Ufbloew:sX--dfl→ioswsiR-pda⩾its0is,viepcal,atifliedvteheawriesttheoxrraiesgstepsefacutlnctiotcoaonlSly,,oLsruipicnshchsthahitozrttf,un(sc,tSio)n- ⋆ This work is supported by the ANR grant HANDY 18-CE40-0010. U : X → R⩾0, called a storage function, such that This work is supported by the ANR grant HANDY 18-CE40-0010. Ulow: X-d→issiRpa⩾t0i,vec,ailfletdhearesteoxraisgtes faulnocctaiollny,Lsuipcshchtihtaztfunction ⋆24T05h-i8s9w63o rCkoipsysruigphpto ©rte2d02b2y Tthhee AuNtRhogrsr.a nTthHis AisN aDn Yop1e8n- CacEc4es0s- 0a0r1ti0c.le unUder: tXhe→ CCR B⩾Y0-,NcCa-NllDed licaenssteo.rage function, such that Peer review under responsibility of International Federation of Automatic Control. 10.1016/j.ifacol.2022.07.254
Publisher Copyright:
© 2022 Elsevier B.V.. All rights reserved.
Financiering
einstsoenatciacolutnot,teaskpeectihaellysawmhpelninfgastbesahmavpiolirngofistnhoetpploastsfiobrlme, counatrraanctteiev)i.tyA, pno∈ta[1b,le∞a)d,viasnotfaigneteorfeosturasseatusptriisngthsattabcliolictky ecinsotsnoednaccouittiiaolnstnoat,rteespakoefecitettnhhaleeplyrsoaawhmceppsenslliienndfggastobnesampahadviigoliirntagolfipstlnahottefoppprllmossiaat,foibtrlme,is claournatrcraaanscette)ieva)i.tndyA,pnveo∈hicta[1ble,le∞-plaa)d,vtoiasnootnfaingigneteoprorfeostubrlemasseatsusp(intriisnwgthhsaitctahbcliLolictpky-ien.gto. ainccocausnet,oefspleocwia-plloywwehreenlefcatsrtosnaimcsp,lingwishnicohtpcoassseibwlee, syunacrhanrotneeiz)a.tAionoitsanboletaredqvuainrteadg.eHoefnocueresaecthuploicsatlhpalattcflorcmk e.g. in case of low-power electronics, in which case we gyounatcrrhaanrcottneieviz)ia.tytA,iopno∈itsa[1nb,ole∞t ar)ed,qviuasinortefadig.netHeoerfneosctueraesaecathuspltoricisnagtlhpsaltatatbcfliolrictmky eta.glk. ionf pcearsieodoifc leovwen-pt-otwriegrgeerleedctcroonnticrso,l,isneew, he.igch., Hcaeseemweles syancsharmonpilzeatainond itsrannostmreitquinirdeedp.eHnednecnetleyacohf alollcaolthpelartpfolramt-eetna..ggtlko.. aiioncfcpocceaaurssnieeot,doeifcspleeovcwweina--ppltl-oytwrwieeghrrgeeeenrlleeefdccattscrtosnatimccrssop,,l,linsnegewi,shen.igcoh.t, pHccoaaessseseemibweleles, syaunacrshaanrmotnepeilz)ea. tAainondoittsraanbnolestmareditqvuaininrdteaedpg.eeHnoedfneocnuetrleysaecothfuaplollicsaotlthpaelatrtcpfloloracmtk-teatlkalo. f(p20er1i3o)d.icMeovreenotv-etrr,igignerpedraccotincter,olt,hseeec,oem.gm.,uHnieceamtieolns foarnmsa, mpalkeinagndthteraanlgsmoriitthinmdefuplelnyddeinsttlryiboufteadll. other plat-ee.tg.ali.n(2c0a1s3e).ofMloowre-opvoewr,erinelpercatcrotinciec,s,the communicatiwone coarnmsa,mpalkeinagndthteraanlgsmoriitthinmdefuplelnyddeinsttlryiboufteadll. other plat-nanetdwuornkknsouwffnersdeflraoyms, iwmhpicehrfemctaiyondsesutrcohy asstatbimiliety-vaorfytinhge 2. PRELIMINARIES neteetawlo. r(k20s1uu3ffff)e.rsMforroemoveiimmr,pienrrffpeecrttaiicootnicsse,sutchhe acsomttiimmmuee-nvviacraytiionng forms, making the2.algPoRErithmLIMfullyINARIEdistribS uted. closed-loop system. While there is abundant literature on For space reasons,2.somePRELIMprelINARIEiminariesS are omitted. An teh.ge.,eNveonwtz-tarriggeteraeld. (c2o0n1t9ro)lanofdmreufeltrie-nagceesntthseyrsetienm, st,ostehee, FFxootrrenspsdpeaceadceverresaiosonnos,f tshoims peappreerliimncilnuadriinesg aalrlenootmatitiotends.thAant tceh.lgoe.s,eeedNvv-eeolonnwottz--pttarrsiiyggsggetteeerrmaeeldd. W(cc2oo0hnn1itl9reoo)tllahnooeffrdemriesufealltrbiie--unaanggcdeeesannntttthsselyyirtsseettirenamm,tusst,,oressteeoheene,, eb.egs.t, oNfoowuzrakrni oewt laeld.g(e2,0n1o9n)eaonfdthreefperroenpcoessedthaeprperinoa, cthoesthine extended version of this paper including all notations that btthh.eestgees.t,leioofNNtvfeeooroounwwauttzz-rrutaakkrrrreinngoocgewwoternllaeeedslddi..dgge,e(ec2r,o0nnna1toonl9lrno)oeelfaaoofnnotfhfdttehhmrreefeeouffppleelltrrrroioope-wpnaigccoosedneeesgssendtatshaapspepyerppsectrritenoosmaa:, ccstthh,oesesstehiienne, beth.eegess.tt,liooNtffeoroowauutzrruakrrenni ocewwotnllaeeslddi.dgge(ee2r,,0nna1ol9ln)oeefaoontffhdttehhrefeofplelroooewpnpicoonessgseeddatshaapepperpecritnoosaa:, ccthoesthiine arxroetreunsseddpeeaddcecanvaernresabioseonnfouosu,fntshdoimsonnpeaarpprreXierilviimn,ciseelneuaedrSinecsgheraarlreslesnetoottmaaltilti.ote(nd2022)s0.t2hA2a)nt. the(1)litenoranlineturearcmonsulideti-srysaltelmofstehtup,e following aspects: arxreeteuncseddoeneddsicandvaenrrsbihoeynfbourufidnthdsisyonsnptaearpmreXisrivion,fcseeletuhedeSincfghoerramrleslsnHetott(aCalt,li.oF(n,2022)sD0t2,h2Ga))t. tbheestliotferoautrukrenocwonlesdidgeer, naollnoefotfhtehefooplllroowpionsgedasappeepccrttossa:: ches in We consider hybrid systems of the form H(C, F, D,G) (12)) nfuolnlylindeisatrrimbuutlteid-saynstdemasysentcuhpro, nous configuration, given by ξ = F(ξ,v), when ξ ∈ C ⊆ X, and ξ ∈ G(ξ), the(12))litennfuoolrannlylliiturenndeeisaatrrcimobnsuuutllidtteiid--esrayynalssttdleemaofsystenhttceuuhppfrolo,,nolowusincgonfigaspecturas:tion, Wgivee ncobynsidedξ˙e=r hFy(bξr,ivd),syswhteenmsξ o∈fnvCthe⊆ foX,rmandHξ(C++,F,∈ DG,G(ξ),) (23)) fimulplyledmisetnrtibabuitleitdyaonnddaisgyitnaclhprolantofoursmcso,nfiguration, gwihven ξby∈ξD=⊆F(Xξ,,vw)h,ewrehevn∈ξ L∈nC i⊆s aXn,eaxnodgeξnou∈s iGn(pξu)t, ((223))) ffimuullnlinepllyyleddmiissaettnrrrtiimbbabuuuittllteeiitd-ysaysonnntedddmaisgyysitennatup,cclhhprroolanntoofouurssmccsoo,nnffiigguration, Wgwhiveeenncoξbyns∈idξ˙˙De=r ⊆hFy(Xbξr,,ivdwh),seryswheteevnmnξ∈sξ Lo∈f∞vvCthi⊆se anfoX,rmexanogendHξ(C+ou, F,∈s DiGn,G(puξ),t) (34)) iumnpknleomwentanbdilittyimoen-vdairgyitinagl pslaamtfoprlimngs, and transmis-(wdhisetnurξba∈ncDe)⊆anXd, Xwh⊆ereRv ∈wLit∞h nisξ a∈n Nex>o0g,esneoeusGionepbuetl ((334))) ifullyumnppknlleeodismwentributetaanbbdiilliittdtyimaonden-vddaaiirsggyyniittinaacgllhprsolaanomtfousprlimncgso,nfiganduratrationsn,mis-g(whdihviseentnurξbbya∈nξ˙cDe=)⊆Fan(Xdξ,,Xvwh)h,⊆erwrehRevnnξξ∈ξwL∈itn∞hvCni⊆sξan∈Xn,Neax>no0dg,eξsn+eoueu∈sGiGone(pubξue)tl, (4) usinoknndoewlanysa,nd time-varying sampling and transmis-(edtiastl.ur(b2a0n12ce))aannddHXeem⊆elRsnetξ wali.t∞nh(v2n02ξ1∈).NFo>r0,thseeeseGhyobebrield (3) ismiopnledmeleanytsa,bility on digital platforms, (wdhisetnurξba∈ncDe)⊆anXd, Xwh⊆ereRv ∈wLith nis a∈n Nexog,esneoeusGionepbuetl (5) sgieonnerdaellastyasb,ilityandperformancepropertiesfor(pos-sytsatel.m(s2,01w2e)aarnediHnteeermesetlesdneξξtinalt.h(e20fo2l1l)o.wFinogrtdhiesssiepahtyibvritidy (45)) sgienoonknnenrdoaeewlllasntyasab,nidlitytimaned-vpaerryfionrgmsaanmcepplirnogpearntdiestrfoarns(mpoiss-(sdytsiasttel.umr(bs2,a0n1w2ce))aranenddiHnXteeerm⊆esetlResdetinwalit.thh(e2n0fo2l1l∈)o.wNFinogr ,tdhsiesesseiepGahtyoibevbritiedyl (5) gsiebnleyraulnsbtoaubnilditeyd)anadttpraecrftoorrms(aansceinprcopnesertniseussf)o.r(pos-syrsotpeemrtsy,,wehiacrheisinctleorseestiendniantutrheetofotllhoewoinngeduissesdipiantiTvieteyl (5) gsiieobnnnleeyrdauelnlasbttyoaasubb,niilldiitteyd)aanadttpraeecrrfftooorrmms(aaannscceeinprcoopneserrttniiseeusssf)o.r(pos-sytrsoatpel.emr(ts2y,0,1ww2eh)iacrhnedisiHncteleoersmeesetilensdentiantault.rhe(e2t0ofo2tl1lh)oe.wFoinongretduhisesesdiepiahntyiTbvrietiedyl Manysiblyworkusnbtroeatundead)subasetttraofctotrshese(asaspinectconss.eAnspusromi). nent p2r0o1p0e)r.ty, which is close in nature to the one used in Teel (5) siebnleyraulnsbtoaubnilditeyd)anadttpraecrftoorrms(aansceinprcoopnesertniseussf)o.r(pos- (p2010)yrsotpeemr.tsy,, wehiacrheisinctleorseestiendniantutrheetofotllhoewoinnge duissesdipiantiTvieteyl MMexaaannmyypwwleooirrskk,sse.ttgrr.eeat,atthaaessuruecbbessetnet oofwfottrhhkeesebseyaaspYsupeectacntss.d.CAAhppenrroomi(m2i0nn2ee1nn)tt, (Defini2010)ti.on 1. Let s : X×Rnnv → R be a supply rate and sibly unbounded) attractors (as in consensus). p2r0o1p0e)r.ty, which is close in navture to the one used in Teel Mewxhaainmcyhpwlperoooirrsvk,isdee.tgrs.eat,imthpaeosurrteacbnesetnttadofwvoatrnhkcesebemyaspeYnutsectaonns.dtCAhhepennromio(n2l0inn2ee1na)tr, S(2010)e⊆finiXt.iobne1a. cLleotsesd:nXon×-eRmnpvty→seRt. bSeysatesmupHplyisrastaeidantdo eMwxxhaaainmmcyhppwllperooirssvk,,isdee.tgrs.e,,iamtthpaeeosrrruteeaccbneesnntetadowwfvooatrrnhkkcebesemyyaeYsnuptseacontnsdd.tCAhhepeennro(mn22li00inn22ee11na))tr,, SDefini⊆ Xtionbe1.a cLetloseds :nXon×-empR ty→setR. beSystaemsupplHyisrastaeidantod wcahsiechwiptrhov(liadregsei)mupnokrntaonwtnatdrvaannscmeimsseinotnsdoenlatyhsewnhoinlelintaeakr-bSe⊆s-fXlowb-ediassicplaostievdenwointh-ermenspvptyectsetto.Sy,sotreminsHhoirst,s(asid,St)o-case with (large) unknown transmission delays while tak-bSDee⊆fsin-fiXltoiwobn-ed1ias.sicLpleaotstievsde:nwXoint×h-erRmespptye→ctsetRto. bSey, soatresmiunpsHphlyoirsrta,st(aesid,aSnt)do-case with (large) unknown transmission delays while tak-fbloews--dflioswsi-pdaitsisviep,atifivtehewriethexriesstps eactlotcoalSly, oLripinschshitozrtf,un(sc,tSio)n-⋆cahsiechwiptrhov(liadregsei)mupnokrntaonwtnatdrvaannscmeimsseinotns doenlatyhsewnhoinlelintaeakr-fbSloew⊆s-dfXlioswsbi-pedaiatsisvicepl,aostifievdtehnewroienth-eexrmiessptpstyeactsloettco.alSlyy, soLtreipminschsHhitozirstf,usn(asicd,tSiot)no-⋆ This work is supported by the ANR grant HANDY 18-CE40-0010. flow: X-d→issiRpa⩾t0i,vec,ailfletdhearesteoxraisgtes faulnocctaiollny,Lsuipcshchtihtaztfunction ⋆caThisse wwithork(lais suprgep)ortedunknboywthen traANnsR gmraisnstioHnANdeDlYay18s-CEwhile40-0010.tak- Ufbloew:sX--dfl→ioswsiR-pda⩾its0is,viepcal,atifliedvteheawriesttheoxrraiesgstepsefacutlnctiotcoaonlSly,,oLsruipicnshchsthahitozrttf,un(sc,tSio)n- ⋆ This work is supported by the ANR grant HANDY 18-CE40-0010. U : X → R⩾0, called a storage function, such that This work is supported by the ANR grant HANDY 18-CE40-0010. Ulow: X-d→issiRpa⩾t0i,vec,ailfletdhearesteoxraisgtes faulnocctaiollny,Lsuipcshchtihtaztfunction ⋆24T05h-i8s9w63o rCkoipsysruigphpto ©rte2d02b2y Tthhee AuNtRhogrsr.a nTthHis AisN aDn Yop1e8n- CacEc4es0s- 0a0r1ti0c.le unUder: tXhe→ CCR B⩾Y0-,NcCa-NllDed licaenssteo.rage function, such that Peer review under responsibility of International Federation of Automatic Control. 10.1016/j.ifacol.2022.07.254