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Volumn 73, Issue 5, 2008, Pages 782-802

Construction of a local and global Lyapunov function using radial basis functions

Author keywords

Basin of attraction; Lyapunov function; Ordinary differential equation; Radial basis functions

Indexed keywords

BIOMECHANICS; BIPED LOCOMOTION; DIFFERENTIAL EQUATIONS; FEEDFORWARD NEURAL NETWORKS; IMAGE SEGMENTATION; LINEAR EQUATIONS; LYAPUNOV FUNCTIONS; ORDINARY DIFFERENTIAL EQUATIONS; RADIAL BASIS FUNCTION NETWORKS; TELECOMMUNICATION NETWORKS;

EID: 54049093299     PISSN: 02724960     EISSN: 14643634     Source Type: Journal    
DOI: 10.1093/imamat/hxn018     Document Type: Article
Times cited : (31)

References (16)
  • 1
    • 54049124486 scopus 로고    scopus 로고
    • BUHMANN, M. D.(2003) Radial Basis Functions: Theory and Implementations. Cambridge: Cambridge University Press.
    • BUHMANN, M. D.(2003) Radial Basis Functions: Theory and Implementations. Cambridge: Cambridge University Press.
  • 2
    • 0003208752 scopus 로고    scopus 로고
    • A regularization of Zubov's equation for robust domains of attraction
    • Nonlinear Control in the Year 2000 A. Isidori, F. Lamnabhi-Lagarrigue & W. Respondek, eds, London: Springer, pp
    • CAMILLI, F., GRÜNE, L. & WIRTH, F.(2000) A regularization of Zubov's equation for robust domains of attraction. Nonlinear Control in the Year 2000 (A. Isidori, F. Lamnabhi-Lagarrigue & W. Respondek, eds). Lecture Notes in Control and Information Sciences, vol. 258. London: Springer, pp. 277-290.
    • (2000) Lecture Notes in Control and Information Sciences , vol.258 , pp. 277-290
    • CAMILLI, F.1    GRÜNE, L.2    WIRTH, F.3
  • 3
    • 0036105218 scopus 로고    scopus 로고
    • A generalization of Zubov's method to perturbed systems
    • CAMILLI, F., GRÜNE, L. & WIRTH, F.(2001) A generalization of Zubov's method to perturbed systems. SIAM J. Control Optim., 40 496-515.
    • (2001) SIAM J. Control Optim , vol.40 , pp. 496-515
    • CAMILLI, F.1    GRÜNE, L.2    WIRTH, F.3
  • 4
    • 54049109606 scopus 로고    scopus 로고
    • GIESL, P.(2004) Approximation of domains of attraction and Lyapunov functions using radial basis functions. Proceedings of the NOLCOS 2004 Conference in Stuttgart (F. Allgöwer, ed.), 2. Germany: VDI/VDE-Gesellschaft Mess- und Automatisierungstechnik, (GMA), pp. 865-870.
    • GIESL, P.(2004) Approximation of domains of attraction and Lyapunov functions using radial basis functions. Proceedings of the NOLCOS 2004 Conference in Stuttgart (F. Allgöwer, ed.), vol. 2. Germany: VDI/VDE-Gesellschaft Mess- und Automatisierungstechnik, (GMA), pp. 865-870.
  • 5
    • 33847760210 scopus 로고    scopus 로고
    • Construction of a global Lyapunov function using radial basis functions with a single operator
    • GIESL, P.(2007a) Construction of a global Lyapunov function using radial basis functions with a single operator. Discrete Contin. Dyn. Syst. Ser B, 7, 101-124.
    • (2007) Discrete Contin. Dyn. Syst. Ser B , vol.7 , pp. 101-124
    • GIESL, P.1
  • 6
    • 34247100563 scopus 로고    scopus 로고
    • Construction of Global Lyapunov Functions Using Radial Basis Functions
    • Berlin: Springer
    • GIESL, P.(2007b) Construction of Global Lyapunov Functions Using Radial Basis Functions. Lecture Notes in Mathematics, vol. 1904. Berlin: Springer.
    • (2007) Lecture Notes in Mathematics , vol.1904
    • GIESL, P.1
  • 7
    • 49449103527 scopus 로고    scopus 로고
    • Meshless collocation: Error estimates with application to dynamical systems
    • GIESL, P. & WENDLAND, H.(2007) Meshless collocation: Error estimates with application to dynamical systems. SIAM J. Numer Anal. 45, 1723-1741.
    • (2007) SIAM J. Numer Anal , vol.45 , pp. 1723-1741
    • GIESL, P.1    WENDLAND, H.2
  • 8
    • 1042267859 scopus 로고    scopus 로고
    • A constructive converse Lyapunov theorem on exponential stability
    • HAFSTEIN, S.(2004) A constructive converse Lyapunov theorem on exponential stability. Discrete Contin. Dyn. Syst., 10, 657-678.
    • (2004) Discrete Contin. Dyn. Syst , vol.10 , pp. 657-678
    • HAFSTEIN, S.1
  • 9
    • 0346419387 scopus 로고
    • Eine Bemerkung zur zweiten Methode von Ljapunov.
    • HAHN, W.(1956) Eine Bemerkung zur zweiten Methode von Ljapunov. Math. Nachr, 14, 349-354.
    • (1956) Math. Nachr , vol.14 , pp. 349-354
    • HAHN, W.1
  • 11
    • 0001570715 scopus 로고
    • Construction of the attraction region by Zubov's method
    • KIRIN, N. E., NELEPIN, R. A. & BAIDAEV, V. N.(1982) Construction of the attraction region by Zubov's method. Differ. Equ., 17 871-880.
    • (1982) Differ. Equ , vol.17 , pp. 871-880
    • KIRIN, N.E.1    NELEPIN, R.A.2    BAIDAEV, V.N.3
  • 12
    • 54049136857 scopus 로고    scopus 로고
    • MASSERA, J. L.(1949) On Liapounoff's conditions of stability. Ann. Math., 50, 705 721.
    • MASSERA, J. L.(1949) On Liapounoff's conditions of stability. Ann. Math., 50, 705 721.
  • 13
    • 0034426073 scopus 로고    scopus 로고
    • A smooth Lyapunov function from a class-KL estimate involving two positive semidefinite functions
    • TEEL, A. R. & PRALY, L.(2000) A smooth Lyapunov function from a class-KL estimate involving two positive semidefinite functions. ESAIM Control Optim. Calc. Var, 5, 313-367.
    • (2000) ESAIM Control Optim. Calc. Var , vol.5 , pp. 313-367
    • TEEL, A.R.1    PRALY, L.2
  • 14
    • 0000764217 scopus 로고    scopus 로고
    • Error estimates for interpolation by compactly supported radial basis functions of minimal degree
    • WENDLAND, H.(1998) Error estimates for interpolation by compactly supported radial basis functions of minimal degree. J. Approx. Iheory 93, 258-272.
    • (1998) J. Approx. Iheory , vol.93 , pp. 258-272
    • WENDLAND, H.1
  • 16
    • 54049137988 scopus 로고    scopus 로고
    • ZUBOV, V.I.(1964) Methods of A.M. Lyapunov and Their Application. Groningen: P. Noordhoff.
    • ZUBOV, V.I.(1964) Methods of A.M. Lyapunov and Their Application. Groningen: P. Noordhoff.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.