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Volumn 52, Issue 7, 2007, Pages 1264-1277

Smooth Lyapunov functions for hybrid systems - Part I: Existence is equivalent to robustness

Author keywords

Hybrid inclusions; Hybrid systems; Measures; Robustness; Smooth Lyapunov functions; Stability

Indexed keywords

HYBRID INCLUSIONS; HYBRID SYSTEM; SMOOTH LYAPUNOV FUNCTION;

EID: 34547094110     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2007.900829     Document Type: Article
Times cited : (102)

References (37)
  • 1
    • 0000381384 scopus 로고    scopus 로고
    • Forward completeness, unboundedness observability, and their Lyapunov characterizations
    • D. Angeli and E. D. Sontag, "Forward completeness, unboundedness observability, and their Lyapunov characterizations," Syst. Contr. Lett., vol. 38, no. 4-5, pp. 209-217, 1999.
    • (1999) Syst. Contr. Lett , vol.38 , Issue.4-5 , pp. 209-217
    • Angeli, D.1    Sontag, E.D.2
  • 2
    • 32144436710 scopus 로고    scopus 로고
    • Global complete observability and output-to-state stability imply the existence of a globally convergent observer
    • A. Astolfi and L. Praly, "Global complete observability and output-to-state stability imply the existence of a globally convergent observer," Math. Contr., Signals, Syst., vol. 18, pp. 32-65, 2006.
    • (2006) Math. Contr., Signals, Syst , vol.18 , pp. 32-65
    • Astolfi, A.1    Praly, L.2
  • 4
    • 0032047505 scopus 로고    scopus 로고
    • Multiple Lyapunov functions and other analysis tools for switched and hybrid systems
    • M. S. Branicky, "Multiple Lyapunov functions and other analysis tools for switched and hybrid systems," IEEE Trans. Autom. Control, vol. 43, no. 4, pp. 475-482, 1998.
    • (1998) IEEE Trans. Autom. Control , vol.43 , Issue.4 , pp. 475-482
    • Branicky, M.S.1
  • 5
    • 34547121325 scopus 로고    scopus 로고
    • Smooth Lyapunov functions for hybrid systems - Part II: (Pre-)Asymptotically stable compact sets
    • accepted for publication
    • C. Cai, A. R. Teel, and R. Goebel, "Smooth Lyapunov functions for hybrid systems - Part II: (Pre-)Asymptotically stable compact sets," IEEE Trans. Autom. Control, 2007, accepted for publication.
    • (2007) IEEE Trans. Autom. Control
    • Cai, C.1    Teel, A.R.2    Goebel, R.3
  • 6
    • 0037408468 scopus 로고    scopus 로고
    • An invariance principle for nonlinear hybrid and impulsive dynamical systems
    • V. Chellaboina, S. P. Bhat, and W. M. Haddad, "An invariance principle for nonlinear hybrid and impulsive dynamical systems," Nonlin. Anal. vol. 53, no. 3-4, pp. 527-550, 2003.
    • (2003) Nonlin. Anal , vol.53 , Issue.3-4 , pp. 527-550
    • Chellaboina, V.1    Bhat, S.P.2    Haddad, W.M.3
  • 7
    • 0002239179 scopus 로고    scopus 로고
    • Asymptotic stability and smooth Lyapunov functions
    • F. H. Clarke, Y. S. Ledyaev, and R. J. Stern, "Asymptotic stability and smooth Lyapunov functions," J. Different. Eq., vol. 149, no. 1, pp. 69-114, 1998.
    • (1998) J. Different. Eq , vol.149 , Issue.1 , pp. 69-114
    • Clarke, F.H.1    Ledyaev, Y.S.2    Stern, R.J.3
  • 9
    • 33646910241 scopus 로고    scopus 로고
    • Perspectives and results on the stability and stabilizability of hybrid systems
    • R. DeCarlo, M. Branicky, S. Pettersson, and B. Lennartson, "Perspectives and results on the stability and stabilizability of hybrid systems," Proc. IEEE, vol. 88, pp. 1069-1082, 2000.
    • (2000) Proc. IEEE , vol.88 , pp. 1069-1082
    • DeCarlo, R.1    Branicky, M.2    Pettersson, S.3    Lennartson, B.4
  • 12
    • 33144463923 scopus 로고    scopus 로고
    • Solution to hybrid inclusions via set and graphical convergence with stability theory applications
    • R. Goebel and A. R. Teel, "Solution to hybrid inclusions via set and graphical convergence with stability theory applications," Automatica, vol. 42, pp. 573-587, 2006.
    • (2006) Automatica , vol.42 , pp. 573-587
    • Goebel, R.1    Teel, A.R.2
  • 14
    • 0033097583 scopus 로고    scopus 로고
    • Stabilization of nonholonomic integrators via logic-based switching
    • J. P. Hespanha and A. S. Morse, "Stabilization of nonholonomic integrators via logic-based switching," Automatica, vol. 35, no. 3, pp. 385-393, 1999.
    • (1999) Automatica , vol.35 , Issue.3 , pp. 385-393
    • Hespanha, J.P.1    Morse, A.S.2
  • 15
    • 3042731389 scopus 로고    scopus 로고
    • Smooth Lyapunov functions and robustness of stability for difference inclusions
    • C. M. Kellett and A. R. Teel, "Smooth Lyapunov functions and robustness of stability for difference inclusions," Syst. Contr. Lett., vol. 52, no. 5, pp. 395-405, 2004.
    • (2004) Syst. Contr. Lett , vol.52 , Issue.5 , pp. 395-405
    • Kellett, C.M.1    Teel, A.R.2
  • 16
    • 33646561839 scopus 로고    scopus 로고
    • On the robustness of K L-stability for difference inclusions: Smooth discrete-time Lyapunov functions
    • C.M. Kellett and A. R. Teel, "On the robustness of K L-stability for difference inclusions: Smooth discrete-time Lyapunov functions," SIAM J. Contr. Optimiz., vol. 44, pp. 777-800, 2005.
    • (2005) SIAM J. Contr. Optimiz , vol.44 , pp. 777-800
    • Kellett, C.M.1    Teel, A.R.2
  • 17
    • 0002585302 scopus 로고
    • On the inversion of Ljapunov's second theorem on stability of motion
    • J. Kurzweil, "On the inversion of Ljapunov's second theorem on stability of motion," Amer. Math. Soci. Translat., ser. 2, vol. 24, pp. 19-77, 1956.
    • (1956) Amer. Math. Soci. Translat., ser. 2 , vol.24 , pp. 19-77
    • Kurzweil, J.1
  • 18
    • 0038491702 scopus 로고    scopus 로고
    • Setvalued hybrid differential equations and stability in terms of two measures
    • V. Lakshmikantham, S. Leela, and A. S. Vatsala, "Setvalued hybrid differential equations and stability in terms of two measures," Int. J. Hybrid Syst., vol. 2, pp. 169-188, 2002.
    • (2002) Int. J. Hybrid Syst , vol.2 , pp. 169-188
    • Lakshmikantham, V.1    Leela, S.2    Vatsala, A.S.3
  • 20
    • 0029775547 scopus 로고    scopus 로고
    • A smooth converse Lyapunov theorem for robust stability
    • Y. Lin, E. D. Sontag, and Y. Wang, "A smooth converse Lyapunov theorem for robust stability," SIAM J. Contr. Optimiz., vol. 34, no. 1, pp. 124-160, 1996.
    • (1996) SIAM J. Contr. Optimiz , vol.34 , Issue.1 , pp. 124-160
    • Lin, Y.1    Sontag, E.D.2    Wang, Y.3
  • 23
    • 0033097304 scopus 로고    scopus 로고
    • Towards a stability theory of general hybrid dynamical systems
    • A. N. Michel and B. Hu, "Towards a stability theory of general hybrid dynamical systems," Automatica, vol. 35, no. 3, pp. 371-384, 1999.
    • (1999) Automatica , vol.35 , Issue.3 , pp. 371-384
    • Michel, A.N.1    Hu, B.2
  • 24
    • 33745771121 scopus 로고    scopus 로고
    • Model checking of hybrid systems: From reachability towards stability
    • A. Podelski and S.Wagner, J. P. Hespanha and A. Tiwari, Eds, HSCC: 9th Int. Workshop
    • A. Podelski and S.Wagner, J. P. Hespanha and A. Tiwari, Eds., "Model checking of hybrid systems: From reachability towards stability," in HSCC: 9th Int. Workshop, 2006, vol. 3927, LNCS, pp. 507-521.
    • (2006) LNCS , vol.3927 , pp. 507-521
  • 25
    • 33645406550 scopus 로고    scopus 로고
    • Perturbed hybrid systems, applications to control theory
    • Berlin, Germany: Springer
    • C. Prieur, "Perturbed hybrid systems, applications to control theory," in Nonlinear and Adaptive Control. Berlin, Germany: Springer, 2003, pp. 285-294.
    • (2003) Nonlinear and Adaptive Control , pp. 285-294
    • Prieur, C.1
  • 26
    • 0242270733 scopus 로고    scopus 로고
    • Robust stabilization of chained systems via hybrid control
    • C. Prieur and A. Astolfi, "Robust stabilization of chained systems via hybrid control," IEEE Trans. Autom. Control, vol. 48, no. 10, pp. 1768-1772, 2003.
    • (2003) IEEE Trans. Autom. Control , vol.48 , Issue.10 , pp. 1768-1772
    • Prieur, C.1    Astolfi, A.2
  • 29
    • 23944472991 scopus 로고    scopus 로고
    • Results on convergence in hybrid systems via detectability and an invariance principle
    • R. G. Sanfelice, R. Goebel, and A. R. Teel, "Results on convergence in hybrid systems via detectability and an invariance principle," in Proc. 24th Amer. Control Conf., 2005, pp. 551-556.
    • (2005) Proc. 24th Amer. Control Conf , pp. 551-556
    • Sanfelice, R.G.1    Goebel, R.2    Teel, A.R.3
  • 30
    • 33745781690 scopus 로고    scopus 로고
    • A feedback control motivation for generalized solutions to hybrid systems
    • R. G. Sanfelice, R. Goebel, and A. R. Teel, J. P. Hespanha and A. Tiwari, Eds, HSCC: 9th Int. Workshop
    • R. G. Sanfelice, R. Goebel, and A. R. Teel, J. P. Hespanha and A. Tiwari, Eds., "A feedback control motivation for generalized solutions to hybrid systems," in HSCC: 9th Int. Workshop, 2006, vol. 3927, LNCS, pp. 522-536.
    • (2006) LNCS , vol.3927 , pp. 522-536
  • 32
    • 0348241184 scopus 로고    scopus 로고
    • Comments on integral variants of ISS
    • E. D. Sontag, "Comments on integral variants of ISS," Syst. Contr. Lett., vol. 34, no. 1-2, pp. 93-100, 1998.
    • (1998) Syst. Contr. Lett , vol.34 , Issue.1-2 , pp. 93-100
    • Sontag, E.D.1
  • 33
    • 0000829463 scopus 로고
    • Differential automata and their simulators
    • L. Tavernini, "Differential automata and their simulators," Nonlin. Anal., Theory, Meth. Applicat., vol. 11, no. 6, pp. 665-683, 1987.
    • (1987) Nonlin. Anal., Theory, Meth. Applicat , vol.11 , Issue.6 , pp. 665-683
    • Tavernini, L.1
  • 34
    • 0034426073 scopus 로고    scopus 로고
    • A smooth Lyapunov function from a class-KL estimate involving two positive simidefinite functions
    • A. R. Teel and L. Praly, "A smooth Lyapunov function from a class-KL estimate involving two positive simidefinite functions," ESAIM: Contr., Optimisation and Calculus of Variations, vol. 5, pp. 313-367, 2000.
    • (2000) ESAIM: Contr., Optimisation and Calculus of Variations , vol.5 , pp. 313-367
    • Teel, A.R.1    Praly, L.2
  • 37
    • 0032050689 scopus 로고    scopus 로고
    • Stability theory for hybrid dynamical systems
    • H. Ye, A.N. Michel, and L. Hou, "Stability theory for hybrid dynamical systems," IEEE Trans. Autom. Control, vol. 43, no. 4, pp. 461-474, 1998.
    • (1998) IEEE Trans. Autom. Control , vol.43 , Issue.4 , pp. 461-474
    • Ye, H.1    Michel, A.N.2    Hou, L.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.