@article{afab3f91b2554c4aba8ad49d901ea685,

title = "Efficient Criteria for Stability of Large-Scale Networked Control Systems",

abstract = "In this paper, we analyze the stochastic stability of a class of large-scale networked control systems. We specifically consider spatially connected linear time-invariant systems whose communication with adjacent subsystems is subject to data losses. We first show that a direct application of the stability theory of Markov jump linear systems provides stability conditions in terms of the eigenvalues of a matrix whose size grows exponentially with the number of subsystems. To overcome this limitation, using the spectrum theory of random matrices, we then derive an alternative stability condition in terms of a matrix whose size grows linearly with the number of subsystems in the network. We illustrate our results with numerical simulations.",

keywords = "data losses, Markov jump linear systems, Networked control systems, random matrices",

author = "Masaki Ogura and Ahmet Cetinkaya and Tomohisa Hayakawa and Preciado, {Victor M.}",

note = "Funding Information: matrices1. INTRODUCTION 1. INTRODUCTION 1. INTRODUCTION NetworΩed control systems have been attracting consid- NetworΩed control systems have been attracting consid- NetworΩed control systems have been attracting consid- erable attention in recent years dΛe to their flexible ar- erable attention in recent years dΛe to their flexible ar- cchlaistseicctaΛlrewsiraenddcolenstsroml sayinsteemnasnc(He ecsopsatnshacometpaalr.e,d20w0i7t)h. chitectΛres and less maintenance costs compared with classical wired control systems (Hespanha et al., 2007). classical wired control systems (Hespanha et al., 2007). Tsyhseteminst,rohdoΛwcetvioenr, oaflstohceaΛnsoetsiotnecohfnniceatlwcohraΩlsleinngteos caornistirnogl systems, however, also caΛses technical challenges arising systems, however, also caΛses technical challenges arising fcraopmaciltoisess. oΣr edecl ayn offinddatina athned lciotenrsattrΛarinetsanonennoertmwoΛrΩs from loss or delay of data and constraints on networΩ caadpvaacnicteietso.wΣaredcsaonlvifningdthiensetphreoblilteemrast,Λarsecan beenosremenoΛins capacities. Σe can find in the literatΛre an enormoΛs advance toward solving these problems, as can be seen in athdevasnΛcrevetyowpaarpderssol(vHinesgptahnehsae eptroabl.l,em20s0,7a;sGcΛapntab,e2s0e1e0n).in advance toward solving these problems, as can be seen in the sΛrvey papers (Hespanha et al., 2007; GΛpta, 2010). the sΛrvey papers (Hespanha et al., 2007; GΛpta, 2010). One of the widely Λsed frameworΩs for the modeling One of the widely Λsed frameworΩs for the modeling One of the widely Λsed frameworΩs for the modeling aMnadrΩaonvaljyΛsmispolfinneeatrwsoyrsΩteedmc(oCntorsotla seytstael.m, s20i1s3g)i,vwenhicbhy ias and analysis of networΩed control systems is given by a Ma calraΩsosvojfΛsmwpitclihnedarlisnyesatremsys(tCeomsstawehtoasel.,s2w0i1tc3h)i,nwghsiicghnaisl a class of switched linear systems whose switching signal a class of switched linear systems whose switching signal is modeled by a time-homogeneoΛs MarΩov process. One is modeled by a time-homogeneoΛs MarΩov process. One oafn tehffeicmienatjomr ordeaeslofnosr ipsactΩheatt lMosaserΩsoavndprdoceelasysessthparotvaidree of the major reasons is that MarΩov processes provide aonbseerffviecdienint cmomodmeΛl nfoicratpioancΩseotvelorsrseeasliastnidc ndeetlwaoyrsΩtsh(aStmaitrhe an efficient model for pacΩet losses and delays that are observed in commΛnications over realistic networΩs (Smith observed in commΛnications over realistic networΩs (Smith and Seiler, 2003). Another reason stems from the well- and Seiler, 2003). Another reason stems from the well- developed theory of MarΩov jΛmp linear systems, which developed theory of MarΩov jΛmp linear systems, which hfeaevdebaecnΩasbtlaebdilitzhaetiornes(eSahricheterasl.,t1o99p9e)r,fsotramb,ilizea.gt.i,onoΛΛntpdΛert have enabled the researchers to perform, e.g., oΛtpΛt feedbacΩ stabilization (Shi et al., 1999), stabilization Λnder feedbacΩ stabilization (Shi et al., 1999), stabilization Λnder random delays in commΛnications (Zhang et al., 2005), raannddHom cdoenlatyrosli(nSeciolemrmanΛdniSceantgioΛnpsta(,Z2h0a0n5g)ienttahle.,co2n0t0e5x)t, random∞ delays in commΛnications (Zhang et al., 2005), and H∞ control (Seiler and SengΛpta, 2005) in the context aonf dneHtw∞orcΩoendtrcooln(tSreoillesryastnedmSse.ngΛpta, 2005) in the context and H∞ control (Seiler and SengΛpta, 2005) in the context of networΩed control systems. Despite the effectiveness of the frameworΩ by MarΩov jΛmp Despite the effectiveness of the frameworΩ by MarΩov jΛmp Despite the effectiveness of the frameworΩ by MarΩov jΛmp linear systems, there is a drawbacΩ that the frameworΩ lilnloewars sΛysstetmo ss,tΛthdeyreoinslya sdmraawllbasccaΩlethsaytsttehmesfrhaamveinwgorΩa allows Λs to stΛdy only small scale systems having a ★allThisowswΛsorktowasssupptΛdyortedonlyinpartsmallbysthecalNeSFsysundertemsgrhanatvsinCgNS-a ★★ This work was supported in part by the NSF under grants CNS- ★3T2h2i2s2waonrdk IwIaSs-1s4u4p7p4o7r0t.ed in part by the NSF under grants CNS- This work was supported in part by the NSF under grants CNS- 1302222 and IIS-1447470. Publisher Copyright: {\textcopyright} 2016",

year = "2016",

doi = "10.1016/j.ifacol.2016.10.365",

language = "English",

volume = "49",

pages = "13--18",

journal = "IFAC-PapersOnLine",

issn = "2405-8963",

publisher = "IFAC Secretariat",

number = "22",

}