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Volumn 17, Issue 4, 2011, Pages 357-365

On a small gain theorem for ISS networks in dissipative Lyapunov form

Author keywords

Dissipativity; Input to state stability; Large scale interconnections; Lyapunov functions; Nonlinear systems; Small gain conditions

Indexed keywords

SYSTEM STABILITY;

EID: 80955135542     PISSN: 09473580     EISSN: None     Source Type: Journal    
DOI: 10.3166/ejc.17.357-365     Document Type: Article
Times cited : (93)

References (24)
  • 1
    • 0017960816 scopus 로고
    • Stability of large-scale nonlinear systems-quadratic-order theory of composite-system method using M-matrices
    • Araki M. Stability of large-scale nonlinear systems-quadratic-order theory of composite-system method using M-matrices. IEEE Trans Autom Control 1978; AC-23: 129-142
    • (1978) IEEE Trans Autom Control , vol.AC-23 , pp. 129-142
    • Araki, M.1
  • 2
    • 0012751750 scopus 로고    scopus 로고
    • Nonsmooth analysis in control theory: A survey
    • Clarke FH. Nonsmooth analysis in control theory: a survey. Eur J Control 2001; 7: 63-78
    • (2001) Eur J Control , vol.7 , pp. 63-78
    • Clarke, F.H.1
  • 6
    • 77957358333 scopus 로고    scopus 로고
    • Small gain theorems for large scale systems and construction of ISS Lyapunov functions
    • Dashkovskiy S, Rüffer B, Wirth F. Small gain theorems for large scale systems and construction of ISS Lyapunov functions. SIAM J Control Optim 2010; 48: 4089-4118
    • (2010) SIAM J Control Optim , vol.48 , pp. 4089-4118
    • Dashkovskiy, S.1    Rüffer, B.2    Wirth, F.3
  • 7
    • 79960931073 scopus 로고    scopus 로고
    • A Lyapunov ISS small gain theorem for strongly connected networks
    • NOLCOS2007, Pretoria, South Africa, August
    • Dashkovskiy S, Rüffer B, Wirth F. A Lyapunov ISS small gain theorem for strongly connected networks. In Proc. 7th IFAC Symposium on Nonlinear Control Systems, NOLCOS2007, pages 283-288, Pretoria, South Africa, August 2007
    • (2007) Proc. 7th IFAC Symposium on Nonlinear Control Systems , pp. 283-288
    • Dashkovskiy, S.1    Rüffer, B.2    Wirth, F.3
  • 8
    • 49449122350 scopus 로고
    • Stability results for nonlinear feedback systems
    • Hill DJ, Moylan PJ. Stability results for nonlinear feedback systems. Automatica 1977; 13: 377-382
    • (1977) Automatica , vol.13 , pp. 377-382
    • Hill, D.J.1    Moylan, P.J.2
  • 9
    • 0036993406 scopus 로고    scopus 로고
    • A constructive proof of ISS small-gain theorem using generalized scaling
    • Las Vegas, Nevada, USA, 2002
    • Ito H. A constructive proof of ISS small-gain theorem using generalized scaling. In Proceedings of the 41st IEEE Conference on Decision and Control, 2002, pages 2286-2291, Las Vegas, Nevada, USA, 2002
    • (2002) Proceedings of the 41st IEEE Conference on Decision and Control , pp. 2286-2291
    • Ito, H.1
  • 10
    • 33750125424 scopus 로고    scopus 로고
    • State-dependent scaling problems and stability of interconnected iISS and ISS systems
    • H. Ito. State-dependent scaling problems and stability of interconnected iISS and ISS systems. IEEE Trans. Automat. Control, 51(10): 1626-1643, 2006
    • (2006) IEEE Trans. Automat. Control , vol.51 , Issue.10 , pp. 1626-1643
    • Ito, H.1
  • 11
    • 39649097615 scopus 로고    scopus 로고
    • Nonlinear small-gain condition covering iISS systems: Necessity and sufficiency from a Lyapunov perspective
    • San Diego, CA, USA
    • Ito H, Jiang Z.-P. Nonlinear small-gain condition covering iISS systems: Necessity and sufficiency from a Lyapunov perspective. In The 45th IEEE Conf. Decision Control, pages 355-360, San Diego, CA, USA, 2006
    • (2006) The 45th IEEE Conf. Decision Control , pp. 355-360
    • Ito, H.1    Jiang, Z.-P.2
  • 12
    • 52449115719 scopus 로고    scopus 로고
    • Small-gain conditions and Lyapunov functions applicable equally to iISS and ISS systems without uniformity assumption
    • Seattle, WA, USA
    • Ito H, Jiang Z.-P. Small-gain conditions and Lyapunov functions applicable equally to iISS and ISS systems without uniformity assumption. In 2008 American Control Conference, pages 2297-2303, Seattle, WA, USA, 2008
    • (2008) 2008 American Control Conference , pp. 2297-2303
    • Ito, H.1    Jiang, Z.-P.2
  • 13
    • 0030218302 scopus 로고    scopus 로고
    • A Lyapunov formulation of the nonlinear small-gain theorem for interconnected ISS systems
    • Jiang Z.-P, Mareels IMY, Wang Y. A Lyapunov formulation of the nonlinear small-gain theorem for interconnected ISS systems. Automatica J IFAC 1996; 32: 1211-1215
    • (1996) Automatica J IFAC , vol.32 , pp. 1211-1215
    • Jiang, Z.-P.1    Mareels, I.M.Y.2    Wang, Y.3
  • 15
  • 17
    • 0017955772 scopus 로고
    • Stability criteria for large-scale systems
    • Moylan PJ, Hill DJ. Stability criteria for large-scale systems. IEEE Trans Autom Control 1978; 23: 143-149
    • (1978) IEEE Trans Autom Control , vol.23 , pp. 143-149
    • Moylan, P.J.1    Hill, D.J.2
  • 18
    • 39549123842 scopus 로고    scopus 로고
    • Dissertation, Fachbereich 3, Mathematik und Informatik, Universität Bremen, Germany, August, Available online
    • Rüffer BS. Monotone Systems, Graphs, and Stability of Large-Scale Interconnected Systems. Dissertation, Fachbereich 3, Mathematik und Informatik, Universität Bremen, Germany, August 2007. Available online: http://nbnresolving.de/urn:nbn:de:gbv:46-diss000109058
    • (2007) Monotone Systems, Graphs, and Stability of Large-Scale Interconnected Systems
    • Rüffer, B.S.1
  • 19
    • 77953130722 scopus 로고    scopus 로고
    • Connection between cooperative positive systems and integral input-to-state stability of large-scale systems
    • Rüffer BS, Kellett CM, Weller SR. Connection between cooperative positive systems and integral input-to-state stability of large-scale systems. Automatica 2010; 46: 1019-1027
    • (2010) Automatica , vol.46 , pp. 1019-1027
    • Rüffer, B.S.1    Kellett, C.M.2    Weller, S.R.3
  • 21
    • 0024647058 scopus 로고
    • Smooth stabilization implies coprime factorization
    • Sontag ED. Smooth stabilization implies coprime factorization. IEEE Trans Autom Control 1989; 34: 435-443
    • (1989) IEEE Trans Autom Control , vol.34 , pp. 435-443
    • Sontag, E.D.1
  • 22
    • 0029430324 scopus 로고
    • Onthe input-to-state stability property
    • Sontag ED. Onthe input-to-state stability property. European J Control 1995; 1: 24-36
    • (1995) European J Control , vol.1 , pp. 24-36
    • Sontag, E.D.1
  • 23
    • 0348241184 scopus 로고    scopus 로고
    • Comments on integral variants of ISS
    • Sontag ED. Comments on integral variants of ISS. Inf Syst Control J 1998; 34: 93-100
    • (1998) Inf Syst Control J , vol.34 , pp. 93-100
    • Sontag, E.D.1
  • 24
    • 34250464350 scopus 로고
    • Dissipative dynamical systems
    • Willems JC. Dissipative dynamical systems. Arch Ration Mech Anal 1972; 45: 321-393
    • (1972) Arch Ration Mech Anal , vol.45 , pp. 321-393
    • Willems, J.C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.