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Input-output-to-state Stability of Nonlinear Switched Systems


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Input-output-to-state Stability of Nonlinear Switched Systems
LIN Xiang-ze12ZOU Yun2
1.College of Engineering,Nanjing Agricultural University,Nanjing 210031,China;2.School of Automation,NUST,Nanjing 210094,China
switched systems input-output-to-state stability state-norm estimator Lyapunov function
To observe and estimate the state of switched systems,sufficient conditions for uniform input-output-to-state stability of nonlinear switched systems are proposed here.In some condition,switched systems are transformed into disturbed systems.Equivalence among uniform input-output-to-state stability of nonlinear switched systems,the existence of smooth Lyapunov function and the existence of the state-norm estimator is proved by using uniform input-output-to-state stability conclusions of disturbed systems.The relationship between uniform input-output-to-state stability of nonlinear switched systems and other stability property is discussed.


[1] BranickyM S. M ultiple Lyapunov functions and o ther analysis too ls for sw itched and hybrid system s[ J]. IEEE Trans on Automat Contr, 1998, 43( 4): 475- 482
[2] Liberzon D, M orse A S. Basic problem s in stab ility and des ign of sw itched system s[ J]. IEEE Con tro l System s, 1999, 19( 5): 59- 70.
[3] H espanha J P, L iberzon D, Ange li D, et a.l Non linea r norm-observability notions and stab ility of sw itched system s[ J] . IEEE Trans on Automa t Contr, 2005, 50 ( 2): 154- 168.
[4] O rlov Y. F inite time stability and robust contro l system s o f uncerta in sw itched system s[ J]. SIAM J Conto l Optim, 2005, 43( 4): 1253- 1271.
[5] Chatterjee D, L iberzon D. S tab ility ana lysis o f dete rm in istic and stochastic sw itched system s v ia a compar-i son pr inc iple and mu ltiple Lyapunov functions[ J] . S IAM J Conto l Optim, 2006, 45( 1) : 174- 206.
[6] Cheng D Z, W ang J H, H u X M. S tab iliza tion of sw itched linear system s v ia LaSa lle. s invar iance pr inc-i ple[ A]. 2007 IEEE Interna tiona l Con ference on Contro l and Autom ation[ C ]. Guang zhou, Ch ina: IEEE, 2007: 1- 6.
[7] Zhao J, H ill D J. Passiv ity and stability of sw itched system s: A m ultiple sto rage function m ethod[ J]. System s& Contro l Letters, 2008, 57( 2) : 158- 164.
[8] W ang J, Cheng D Z. Ex tensions of LaSa lle. s inv ariant pr inciple for sw itched non linear system s[ A]. Proceedings of the 17th IFAC W o rld Congress [ C ]. Seou,l Ko rea: IFAC, 2008: 14397- 14402.
[9] Bem po rad A, Ferrar-i Trecate G, M orar iM. Observability and contro llab ility of p iecew ise a ffine and hybr id system s [ J]. IEEE Trans on Autom at Contr, 2000, 45( 10): 1864- 1876.
[10] Sun Z, Ge S S, Lee T H. Contro llability and reachab ility criter ia fo r sw itched linear system s[ J]. Autom atica, 2002, 38( 5): 775- 786.
[11] 程代展, 郭宇骞. 切换系统进展[ J]. 控制理论与应 用, 2005, 22( 6) : 954- 960.
[12] L in H, An tsaklis P J. S tab ility and stabilizability of sw itched linear sy stem s: A surv ey on recen t resu lts [ J]. IEEE Transactions on Autom atic Contro,l 2009, 54( 2): 308- 322.
[13] Cao M, M orse A S. Dwe l-l time sw itch ing [ J]. System s and Con tro l Letters, 2010, 59( 1): 57- 65.
[14] H an T, Ge S S, Lee T H. Persistent dwe l-l tim e sw itched nonlinear system s: Va riation parad igm and gauge des ign [ J] . IEEE T ransactions on Au tom atic Contro,l 2010, 55( 2) : 321- 337.
[15] 方志明, 向峥嵘, 陈庆伟. 一类参数不确定切换Lurie 系统鲁棒稳定性分析[ J]. 南京理工大学学报 (自然科学版), 2009, 33( 2): 152- 155.
[16] Bem po rad A, M orariM. Contro l o f system s integ ra ting log ic, dynam ics, and constraints [ J ]. Automa tica, 1999, 35( 3): 407- 427.
[17] Sun Z, Ge S S. Ana lysis and synthes is o f sw itched linear contro l system s[ J]. Autom atica, 2005, 41 ( 2 ): 181- 195.
[18] 付主木, 费树岷, 薄煜明, 等. 不确定切换奇异系统 的鲁棒H ] 控制[ J]. 南京理工大学学报( 自然科学 版), 2008, 32( 3): 269- 273.
[19] H espanha J P. Unifo rm stability of sw itched linear system s: Ex tensions o f LaSalle. s invariance pr inciple[ J]. IEEE Trans on Au tom at Contr, 49( 4): 470- 482.
[20] Sontag E D, W angY. Outpu t-to-state stab ility and detectability o f nonlinea r systems[ J]. System s& Contro l Letters, 1997, 29( 5) : 279- 290.
[21] K richm anM, Sontag E D, W ang Y. Input-output- tosta te stab ility [ J]. SIAM J Control Optim, 2001, 39 ( 6): 1874- 1928.
[22] Liberzon D. ISS and integra l ISS disturbance attenuation w ith bounded contro ls [ A ]. Pro ceedings o f the 38 th Conference on Dec ision and Contro l[ C ]. Phoen ix, Arizona, USA: IEEE, 1999: 2501- 2506.
[23] M anc illa-Aguilar J L, Garc ia R A. On converse Lyapunov theorems for ISS and iISS sw itched nonlinea r system s[ J]. Sys& ContrLetters, 2001, 42( 1): 47- 53.
[24] M ancilla-Agu ilar J L. A condition for the stability o f sw itched nonlinear system s[ J]. IEEE Trans Autom at Con t Lette rs, 2000, 45( 11): 2077- 2079.
[25] Sontag E D, W ang Y. Detec tab ility o f non linear system s[ A] . Proc Con f on In fo rm ation Science and System s( CISS.96) [ C]. Pr inceton, NJ, USA: Pr ince ton, 1996: 1031- 1036.
[26] Munkres R J. Topo logy: A first course [M ]. New Yo rk, USA: Prentice-H a l,l Eng lew ood C liffs, 1998. 308


Last Update: 2010-06-30