메뉴 건너뛰기




Volumn 55, Issue 11, 2008, Pages 3528-3541

Lyapunov method and convergence of the full-range model of CNNs

Author keywords

Cellular neural networks (CNNs); Convergence; Differential variational inequalities (DVIs); Full range (FR) model; LaSalle's invariance principle; Set valued derivative

Indexed keywords

ASYMPTOTIC STABILITY; LYAPUNOV FUNCTIONS; LYAPUNOV METHODS; VARIATIONAL TECHNIQUES;

EID: 58049206270     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCSI.2008.925820     Document Type: Article
Times cited : (31)

References (40)
  • 1
    • 0024088955 scopus 로고
    • Cellular neural networks: Theory
    • Oct
    • L. O. Chua and L. Yang, "Cellular neural networks: Theory," IEEE Trans. Circuits Syst., vol. 35, no. 10, pp. 1257-1272, Oct. 1988.
    • (1988) IEEE Trans. Circuits Syst , vol.35 , Issue.10 , pp. 1257-1272
    • Chua, L.O.1    Yang, L.2
  • 3
    • 53849094420 scopus 로고    scopus 로고
    • Special issue on CNN technology and active wave computing
    • May
    • B. E. Shi, P. Arena, and A. Zarandi, "Special issue on CNN technology and active wave computing," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 51, no. 5, pp. 939-947, May 2004.
    • (2004) IEEE Trans. Circuits Syst. I, Reg. Papers , vol.51 , Issue.5 , pp. 939-947
    • Shi, B.E.1    Arena, P.2    Zarandi, A.3
  • 4
    • 32344437744 scopus 로고    scopus 로고
    • Immune response inspired spatial-temporal target detection algorithms with CNN-UM
    • Jan/Feb
    • G. Cserey, A. Falus, and T. Roska, "Immune response inspired spatial-temporal target detection algorithms with CNN-UM," Int. J. Circuit Theory Appl., vol. 34, no. 1, pp. 21-47, Jan/Feb. 2006.
    • (2006) Int. J. Circuit Theory Appl , vol.34 , Issue.1 , pp. 21-47
    • Cserey, G.1    Falus, A.2    Roska, T.3
  • 5
    • 58049208869 scopus 로고    scopus 로고
    • Special issue on CNN technology (Part 1)
    • Jan
    • T. Roska, P. Arena, and C. Rekeczky, "Special issue on CNN technology (Part 1)," Int. J. Circuit Theory Appl., vol. 34, no. 1, pp. 127-140, Jan. 2006.
    • (2006) Int. J. Circuit Theory Appl , vol.34 , Issue.1 , pp. 127-140
    • Roska, T.1    Arena, P.2    Rekeczky, C.3
  • 6
    • 0000428652 scopus 로고
    • Special issue on nonlinear waves, patterns and spatio-temporal chaos in dynamic arrays
    • Oct
    • L. O. Chua, "Special issue on nonlinear waves, patterns and spatio-temporal chaos in dynamic arrays," IEEE Trans. Circuits Syst. I, vol. 42, no. 10, pp. 557-823, Oct. 1995.
    • (1995) IEEE Trans. Circuits Syst. I , vol.42 , Issue.10 , pp. 557-823
    • Chua, L.O.1
  • 7
    • 0037560994 scopus 로고    scopus 로고
    • New spatial-temporal patterns and the first programmable on-chip bifurcation test bed
    • May
    • I. Petrás, T. Roska, and L. O. Chua, "New spatial-temporal patterns and the first programmable on-chip bifurcation test bed," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 50, no. 5, pp. 619-633, May 2003.
    • (2003) IEEE Trans. Circuits Syst. I, Fundam. Theory Appl , vol.50 , Issue.5 , pp. 619-633
    • Petrás, I.1    Roska, T.2    Chua, L.O.3
  • 13
    • 34547988902 scopus 로고    scopus 로고
    • Dynamical analysis of full-range cellular neural networks by exploiting differential variational inequalities
    • Aug
    • G. D. Sandre, M. Forti, P. Nistri, and A. Premoli, "Dynamical analysis of full-range cellular neural networks by exploiting differential variational inequalities," IEEE Trans. Circuits Syst. I, Reg. Papers vol. 54, no. 8, pp. 1736-1749, Aug. 2007.
    • (2007) IEEE Trans. Circuits Syst. I, Reg. Papers , vol.54 , Issue.8 , pp. 1736-1749
    • Sandre, G.D.1    Forti, M.2    Nistri, P.3    Premoli, A.4
  • 14
    • 0141886036 scopus 로고    scopus 로고
    • Comparison between the dynamic behaviour of Chua-Yang and full-range cellular neural networks
    • Sep./Oct
    • F. Corinto and M. Gilli, "Comparison between the dynamic behaviour of Chua-Yang and full-range cellular neural networks," Int. J. Circuit Theory Appl., vol. 31, no. 5, pp. 423-441, Sep./Oct. 2003.
    • (2003) Int. J. Circuit Theory Appl , vol.31 , Issue.5 , pp. 423-441
    • Corinto, F.1    Gilli, M.2
  • 15
    • 0028497846 scopus 로고
    • Lyapunov stability theory of nonsmooth systems
    • Sep
    • D. Shevitz and B. Paden, "Lyapunov stability theory of nonsmooth systems," IEEE Trans. Autom. Control, vol. 39, no. 9, pp. 1910-1914, Sep. 1994.
    • (1994) IEEE Trans. Autom. Control , vol.39 , Issue.9 , pp. 1910-1914
    • Shevitz, D.1    Paden, B.2
  • 16
    • 0033276564 scopus 로고    scopus 로고
    • Stability and stabilization of discontinuous systems and nonsmooth Lyapunov functions
    • A. Bacciotti and F. Ceragioli, "Stability and stabilization of discontinuous systems and nonsmooth Lyapunov functions," Esaim, COCV vol. 4, pp. 361-376, 1999.
    • (1999) Esaim, COCV , vol.4 , pp. 361-376
    • Bacciotti, A.1    Ceragioli, F.2
  • 20
    • 0001343175 scopus 로고
    • Entrainement unilatéral, lignes de descente, fonctions Lipschitziennes non pathologiques
    • M. Valadier, "Entrainement unilatéral, lignes de descente, fonctions Lipschitziennes non pathologiques," Comptes Rendu Academie des Sciences. Series I, Mathematique. Paris, vol. 8, pp. 241-244, 1989.
    • (1989) Comptes Rendu Academie des Sciences. Series I, Mathematique. Paris , vol.8 , pp. 241-244
    • Valadier, M.1
  • 21
    • 31144478341 scopus 로고    scopus 로고
    • Nonpathological Lyapunov functions and discontinuous Carathéodory systems
    • Mar
    • A. Bacciotti and F. Ceragioli, "Nonpathological Lyapunov functions and discontinuous Carathéodory systems," Automatica, vol. 42, no. 3, pp. 453-458, Mar. 2006.
    • (2006) Automatica , vol.42 , Issue.3 , pp. 453-458
    • Bacciotti, A.1    Ceragioli, F.2
  • 22
    • 38849089467 scopus 로고    scopus 로고
    • Differential variational inequalities
    • Jan
    • J. Pang and D. Stewart, "Differential variational inequalities," Math. Program., Ser. A, vol. 113, no. 2, pp. 345-424, Jan. 2008.
    • (2008) Math. Program., Ser. A , vol.113 , Issue.2 , pp. 345-424
    • Pang, J.1    Stewart, D.2
  • 23
    • 0004267646 scopus 로고
    • Princeton, NJ: Princeton Univ. Press
    • R. T. Rockafellar, Convex Analysis. Princeton, NJ: Princeton Univ. Press, 1970.
    • (1970) Convex Analysis
    • Rockafellar, R.T.1
  • 24
    • 0003608428 scopus 로고
    • Differential Equations With Discontinuous Right-Hand Side
    • Mathematics and its Applications , Boston, MA: Kluwer
    • A. F. Filippov, Differential Equations With Discontinuous Right-Hand Side. Mathematics and its Applications (Soviet Series). Boston, MA: Kluwer, 1988.
    • (1988) Soviet Series
    • Filippov, A.F.1
  • 26
    • 0025632457 scopus 로고
    • Stability of a class of nonreciprocal cellular neural networks
    • Dec
    • L. O. Chua and T. Roska, "Stability of a class of nonreciprocal cellular neural networks," IEEE Trans. Circuits Syst., vol. 37, no. 12, pp. 1520-1527, Dec. 1990.
    • (1990) IEEE Trans. Circuits Syst , vol.37 , Issue.12 , pp. 1520-1527
    • Chua, L.O.1    Roska, T.2
  • 27
    • 0032138886 scopus 로고    scopus 로고
    • An approach to information propagation in 1-D cellular neural networks. Part I: Local diffusion
    • Aug
    • P. Thiran, G. Setti, and M. Hasler, "An approach to information propagation in 1-D cellular neural networks. Part I: Local diffusion," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 45, no. 8, pp. 777-789, Aug. 1998.
    • (1998) IEEE Trans. Circuits Syst. I, Fundam. Theory Appl , vol.45 , Issue.8 , pp. 777-789
    • Thiran, P.1    Setti, G.2    Hasler, M.3
  • 29
    • 0029345226 scopus 로고
    • New conditions for global stability of neural networks with application to linear and quadratic programming problems
    • Jul
    • M. Forti and A. Tesi, "New conditions for global stability of neural networks with application to linear and quadratic programming problems," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 42, no. 7, pp. 354-366, Jul. 1995.
    • (1995) IEEE Trans. Circuits Syst. I, Fundam. Theory Appl , vol.42 , Issue.7 , pp. 354-366
    • Forti, M.1    Tesi, A.2
  • 30
    • 0037274395 scopus 로고    scopus 로고
    • Absolute exponential stability of a class of continuous-time recurrent neural networks
    • Jan
    • S. Hu and J. Wang, "Absolute exponential stability of a class of continuous-time recurrent neural networks," IEEE Trans. Neural Netw. vol. 14, no. 1, pp. 35-45, Jan. 2003.
    • (2003) IEEE Trans. Neural Netw , vol.14 , Issue.1 , pp. 35-45
    • Hu, S.1    Wang, J.2
  • 31
    • 0037928710 scopus 로고    scopus 로고
    • New conditions on global stability of Cohen-Grossberg neural networks
    • May
    • W. Lu and T. Chen, "New conditions on global stability of Cohen-Grossberg neural networks," Neural Comput., vol. 15, no. 5, pp. 1173-1189, May 2003.
    • (2003) Neural Comput , vol.15 , Issue.5 , pp. 1173-1189
    • Lu, W.1    Chen, T.2
  • 32
    • 1242308790 scopus 로고    scopus 로고
    • Deriving sufficient conditions for global asymptotic stability of delayed neural networks via nonsmooth analysis
    • Jan
    • H. Qi and L. Qi, "Deriving sufficient conditions for global asymptotic stability of delayed neural networks via nonsmooth analysis," IEEE Trans. Neural Netw., vol. 15, no. 1, pp. 99-109, Jan. 2004.
    • (2004) IEEE Trans. Neural Netw , vol.15 , Issue.1 , pp. 99-109
    • Qi, H.1    Qi, L.2
  • 33
    • 14644434391 scopus 로고    scopus 로고
    • Global asymptotic and robust stability of recurrent neural networks with time delays
    • Feb
    • J. Cao and J. Wang, "Global asymptotic and robust stability of recurrent neural networks with time delays," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 52, no. 2, pp. 417-426, Feb. 2005.
    • (2005) IEEE Trans. Circuits Syst. I, Reg. Papers , vol.52 , Issue.2 , pp. 417-426
    • Cao, J.1    Wang, J.2
  • 34
    • 0000885375 scopus 로고
    • Systems of differential equations which are competitive or cooperative. I: Limit sets
    • M. W. Hirsch, "Systems of differential equations which are competitive or cooperative. I: Limit sets," SIAM J. Math. Anal., vol. 13, pp. 167-179, 1982.
    • (1982) SIAM J. Math. Anal , vol.13 , pp. 167-179
    • Hirsch, M.W.1
  • 35
    • 0033131573 scopus 로고    scopus 로고
    • Complete stability for standard cellular neural networks
    • S. S. Lin and C. W. Shih, "Complete stability for standard cellular neural networks," Int. J. Bifurc. Chaos, vol. 9, pp. 909-918, 1999.
    • (1999) Int. J. Bifurc. Chaos , vol.9 , pp. 909-918
    • Lin, S.S.1    Shih, C.W.2
  • 36
    • 33750544696 scopus 로고    scopus 로고
    • The Lojasiewicz exponent at an equilibrium point of a standard CNN is 1/2
    • Aug
    • M. Forti and A. Tesi, "The Lojasiewicz exponent at an equilibrium point of a standard CNN is 1/2," Int. J. Bifurc. Chaos, vol. 16, no. 8, pp. 2191-2205, Aug. 2006.
    • (2006) Int. J. Bifurc. Chaos , vol.16 , Issue.8 , pp. 2191-2205
    • Forti, M.1    Tesi, A.2
  • 37
    • 38249012613 scopus 로고
    • Recent directions in matrix stability
    • D. Hershkowitz, "Recent directions in matrix stability," Linear Algebra Appl., vol. 171, pp. 161-186, 1992.
    • (1992) Linear Algebra Appl , vol.171 , pp. 161-186
    • Hershkowitz, D.1
  • 38
    • 47749140435 scopus 로고    scopus 로고
    • On global exponential stability of standard and full-range CNNs
    • Jul
    • M. Di Marco, M. Forti, M. Grazzini, and L. Pancioni, "On global exponential stability of standard and full-range CNNs," Int. J. Circuit Theory Appl., vol. 36, no. 5/6, pp. 653-680, Jul. 2008.
    • (2008) Int. J. Circuit Theory Appl , vol.36 , Issue.5-6 , pp. 653-680
    • Di Marco, M.1    Forti, M.2    Grazzini, M.3    Pancioni, L.4
  • 39
    • 0033332523 scopus 로고    scopus 로고
    • Estimate of exponential convergence rate and exponential stability for neural networks
    • Nov
    • Y. Zhang, P. Heng, and A. Fu, "Estimate of exponential convergence rate and exponential stability for neural networks," IEEE Trans. Neural Netw., vol. 10, no. 6, pp. 1487-1493, Nov. 1999.
    • (1999) IEEE Trans. Neural Netw , vol.10 , Issue.6 , pp. 1487-1493
    • Zhang, Y.1    Heng, P.2    Fu, A.3
  • 40
    • 0035272288 scopus 로고    scopus 로고
    • Global exponential stability of neural networks with globally Lipschitz continuous activations and its application to linear variational inequality problem
    • Mar
    • X. Liang and J. Si, "Global exponential stability of neural networks with globally Lipschitz continuous activations and its application to linear variational inequality problem," IEEE Trans. Neural Netw., vol. 12, no. 2, pp. 349-359, Mar. 2001.
    • (2001) IEEE Trans. Neural Netw , vol.12 , Issue.2 , pp. 349-359
    • Liang, X.1    Si, J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.