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Volumn 53, Issue 3, 2008, Pages 734-748

Smooth Lyapunov functions for hybrid systems part II: (Pre)asymptotically stable compact sets

Author keywords

Asymptotic stability; Hybrid systems; Robustness; Smooth Lyapunov functions

Indexed keywords

FEEDBACK CONTROL; LYAPUNOV FUNCTIONS; ROBUSTNESS (CONTROL SYSTEMS);

EID: 42649113750     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2008.919257     Document Type: Article
Times cited : (172)

References (37)
  • 2
    • 23944504793 scopus 로고    scopus 로고
    • Converse Lyapunov theorems and robust asymptotic stability for hybrid systems
    • C. Cai, A. R. Teel, and R. Goebel, "Converse Lyapunov theorems and robust asymptotic stability for hybrid systems," in Proc. 24th Amer. Control Conf., 2005, pp. 12-17.
    • (2005) Proc. 24th Amer. Control Conf , pp. 12-17
    • Cai, C.1    Teel, A.R.2    Goebel, R.3
  • 4
    • 34547094110 scopus 로고    scopus 로고
    • Smooth Lyapunov functions for hybrid systems Part I: Existence is equivalent to robustness
    • Jul
    • C. Cai, A. R. Teel, and R. Goebel, "Smooth Lyapunov functions for hybrid systems Part I: Existence is equivalent to robustness," IEEE Trans. Autom. Control, vol 52, no. 7, pp. 1264-1277, Jul. 2007.
    • (2007) IEEE Trans. Autom. Control , vol.52 , Issue.7 , pp. 1264-1277
    • Cai, C.1    Teel, A.R.2    Goebel, R.3
  • 5
    • 0345275284 scopus 로고    scopus 로고
    • Pullback attractors in dissipative nonautonomous differential equations under discretization
    • D. N. Cheban, P. E. Kloeden, and B. Schmalfu, "Pullback attractors in dissipative nonautonomous differential equations under discretization," J. Dyn. Differential Equations, vol. 13, no. 1, pp. 185-213, 2001.
    • (2001) J. Dyn. Differential Equations , vol.13 , Issue.1 , pp. 185-213
    • Cheban, D.N.1    Kloeden, P.E.2    Schmalfu, B.3
  • 6
    • 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. Differential Equations, vol. 149, no. 1, pp. 69-114, 1998.
    • (1998) J. Differential Equations , vol.149 , Issue.1 , pp. 69-114
    • Clarke, F.H.1    Ledyaev, Y.S.2    Stern, R.J.3
  • 7
    • 33645423168 scopus 로고    scopus 로고
    • A trajectory-space approach to hybrid systems
    • presented at the, Berlin, Germany
    • P. Collins, "A trajectory-space approach to hybrid systems," presented at the 16th Int. Symp. Math. Theory Netw. Syst., Berlin, Germany, 2004.
    • (2004) 16th Int. Symp. Math. Theory Netw. Syst
    • Collins, P.1
  • 8
    • 0026204666 scopus 로고
    • Adding an integrator for the stabilization problem
    • J.-M. Coron and L. Praly, "Adding an integrator for the stabilization problem," Syst. Control Lett., vol. 17, no. 2, pp. 89-104, 1991.
    • (1991) Syst. Control Lett , vol.17 , Issue.2 , pp. 89-104
    • Coron, J.-M.1    Praly, L.2
  • 11
    • 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
  • 16
    • 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
  • 17
    • 84968512344 scopus 로고
    • Singular perturbations on the infinite interval
    • F. C. Hoppensteadt, "Singular perturbations on the infinite interval," Trans. Amer. Math. Soc., vol. 123, pp. 521-535, 1966.
    • (1966) Trans. Amer. Math. Soc , vol.123 , pp. 521-535
    • Hoppensteadt, F.C.1
  • 18
    • 33646561839 scopus 로고    scopus 로고
    • On the robustness of KL-stability for difference inclusions: Smooth discrete-time Lyapunov functions
    • C. Kellett ad A. R. Teel, "On the robustness of KL-stability for difference inclusions: Smooth discrete-time Lyapunov functions," SIAM J. Control Optim., vol. 44, no. 3, pp. 777-800, 2005.
    • (2005) SIAM J. Control Optim , vol.44 , Issue.3 , pp. 777-800
    • Kellett ad, C.1    Teel, A.R.2
  • 19
    • 0013263729 scopus 로고    scopus 로고
    • Advances in converse and control Lyapunov functions,
    • Ph.D. dissertation, Univ. California, Santa Barbara
    • C. M. Kellett, "Advances in converse and control Lyapunov functions," Ph.D. dissertation, Univ. California, Santa Barbara, 2002.
    • (2002)
    • Kellett, C.M.1
  • 20
    • 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. Control Lett., vol. 52, no. 5, pp. 395-405, 2004.
    • (2004) Syst. Control Lett , vol.52 , Issue.5 , pp. 395-405
    • Kellett, C.M.1    Teel, A.R.2
  • 21
    • 0033197348 scopus 로고    scopus 로고
    • A Lyapunov characterization of robust stabilization
    • Y. S. Ledyaev and E. D. Sontag, "A Lyapunov characterization of robust stabilization," Nonlinear Anal., vol. 37, pp. 813-840, 1999.
    • (1999) Nonlinear Anal , vol.37 , pp. 813-840
    • Ledyaev, Y.S.1    Sontag, E.D.2
  • 23
    • 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. Control Optimization, vol. 34, no. 1, pp. 124-160, 1996.
    • (1996) SIAM J. Control Optimization , vol.34 , Issue.1 , pp. 124-160
    • Lin, Y.1    Sontag, E.D.2    Wang, Y.3
  • 26
    • 10244242681 scopus 로고    scopus 로고
    • Global asymptotic controllability implies input-to-state stabilizationtems
    • M. Malisoff, L. Rifford, and E. Sontag, "Global asymptotic controllability implies input-to-state stabilizationtems," SIAM J. Control Optimization, vol. 42, no. 6, pp. 2221-2238, 2004.
    • (2004) SIAM J. Control Optimization , vol.42 , Issue.6 , pp. 2221-2238
    • Malisoff, M.1    Rifford, L.2    Sontag, E.3
  • 27
    • 84906329012 scopus 로고
    • Design of stable control systems subject to parametric perturbations
    • A. M. Meilakhs, "Design of stable control systems subject to parametric perturbations," Autom. Remote Control, vol. 39, no. 10, pp. 1409-14180, 1978.
    • (1978) Autom. Remote Control , vol.39 , Issue.10 , pp. 1409-14180
    • Meilakhs, A.M.1
  • 28
    • 0242270733 scopus 로고    scopus 로고
    • Robust stabilization of chained systems via hybrid control
    • Oct
    • C. Prieur and A. Astolfi, "Robust stabilization of chained systems via hybrid control," IEEE Trans. Autom. Control, vol. 48, no. 10, pp. 1768-1772, Oct. 2003.
    • (2003) IEEE Trans. Autom. Control , vol.48 , Issue.10 , pp. 1768-1772
    • Prieur, C.1    Astolfi, A.2
  • 29
    • 33745784418 scopus 로고    scopus 로고
    • Results on robust stabilization of asymptotically controllable systems by hybrid feedback
    • C. Prieur, R. Goebel, and A. R. Teel, "Results on robust stabilization of asymptotically controllable systems by hybrid feedback," in Proc. 44th IEEE Conf. Decision Control, 2005, pp. 2598-2603.
    • (2005) Proc. 44th IEEE Conf. Decision Control , pp. 2598-2603
    • Prieur, C.1    Goebel, R.2    Teel, A.R.3
  • 31
    • 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
  • 32
    • 0024647058 scopus 로고
    • Smooth stabilization implies coprime factorization
    • Apr
    • E. Sontag, "Smooth stabilization implies coprime factorization," IEEE Trans. Autom. Control, vol. 34, no. 4, pp. 435-443, Apr. 1989.
    • (1989) IEEE Trans. Autom. Control , vol.34 , Issue.4 , pp. 435-443
    • Sontag, E.1
  • 33
    • 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: Control, Optim. Calculus Variations, vol. 5, pp. 313-367, 2000.
    • (2000) ESAIM: Control, Optim. Calculus Variations , vol.5 , pp. 313-367
    • Teel, A.R.1    Praly, L.2
  • 34
    • 0024865167 scopus 로고
    • Sufficient Lyapunov-like conditions for stabilization
    • J. Tsinias, "Sufficient Lyapunov-like conditions for stabilization," Math. Control Signals Syst., vol. 2, no. 4, pp. 343-357, 1989.
    • (1989) Math. Control Signals Syst , vol.2 , Issue.4 , pp. 343-357
    • Tsinias, J.1
  • 35
    • 14344266156 scopus 로고    scopus 로고
    • Discrete-time homogeneous Lyapunov functions for homogeneous difference inclusions
    • S. E. Tuna and A. R. Teel, "Discrete-time homogeneous Lyapunov functions for homogeneous difference inclusions," in Proc. 43rd IEEE Conf. Decision Control, 2004, pp. 1606-1610.
    • (2004) Proc. 43rd IEEE Conf. Decision Control , pp. 1606-1610
    • Tuna, S.E.1    Teel, A.R.2
  • 37
    • 0032050689 scopus 로고    scopus 로고
    • Stability theory for hybrid dynamical systems
    • Apr
    • 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, Apr. 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.