메뉴 건너뛰기




Volumn 14, Issue 1, 2003, Pages 35-45

Absolute exponential stability of a class of continuous-time recurrent neural networks

Author keywords

Absolute exponential stability (AEST); Additive diagonal stability; Diagonal semistability; Global exponential stability; H matrix; Neural networks

Indexed keywords

DIFFERENTIATION (CALCULUS); FUNCTIONS; MATRIX ALGEBRA; VECTORS;

EID: 0037274395     PISSN: 10459227     EISSN: None     Source Type: Journal    
DOI: 10.1109/TNN.2002.806954     Document Type: Article
Times cited : (62)

References (34)
  • 2
    • 0032070578 scopus 로고    scopus 로고
    • A comment on 'comments on 'necessary and sufficient condition for absolute stability of neural networks
    • May
    • _, "A comment on 'comments on 'necessary and sufficient condition for absolute stability of neural networks"," IEEE Trans. Circuits Syst. I, vol. 45, pp. 595-596, May 1998.
    • (1998) IEEE Trans. Circuits Syst. I , vol.45 , pp. 595-596
  • 3
    • 0033730977 scopus 로고    scopus 로고
    • Global asymptotic stability of a class of dynamical neural networks
    • Apr.
    • S. Arik, "Global asymptotic stability of a class of dynamical neural networks," IEEE Trans. Circuits Syst. I, vol. 47, pp. 568-571, Apr. 2000.
    • (2000) IEEE Trans. Circuits Syst. I , vol.47 , pp. 568-571
    • Arik, S.1
  • 4
    • 0033723205 scopus 로고    scopus 로고
    • A sufficient condition for absolute stability of a larger class of dynamical neural networks
    • May
    • S. Arik and V. Tavsanoglu, "A sufficient condition for absolute stability of a larger class of dynamical neural networks," IEEE Trans. Circuits Syst. I, vol. 47, pp. 758-760, May 2000.
    • (2000) IEEE Trans. Circuits Syst. I , vol.47 , pp. 758-760
    • Arik, S.1    Tavsanoglu, V.2
  • 5
    • 0026883588 scopus 로고
    • A condition for global convergence of a class of symmetric neural networks
    • June
    • M. Forti, S. Manetti, and M. Marini, "A condition for global convergence of a class of symmetric neural networks," IEEE Trans. Circuits Syst. I, vol. 39, pp. 480-483, June 1992.
    • (1992) IEEE Trans. Circuits Syst. I , vol.39 , pp. 480-483
    • Forti, M.1    Manetti, S.2    Marini, M.3
  • 6
    • 0028465673 scopus 로고
    • Necessary and sufficient condition for absolute stability of neural networks
    • June
    • _, "Necessary and sufficient condition for absolute stability of neural networks," IEEE Trans. Circuits Syst. I, vol. 41, pp. 491-494, June 1994.
    • (1994) IEEE Trans. Circuits Syst. I , vol.41 , pp. 491-494
  • 8
    • 0029345226 scopus 로고
    • New condition for global stability of neural networks with application to linear and quadratic programming problems
    • July
    • M. Forti and A. Tesi, "New condition for global stability of neural networks with application to linear and quadratic programming problems," IEEE Trans. Circuits Syst. I, vol. 42, pp. 354-366, July 1995.
    • (1995) IEEE Trans. Circuits Syst. I , vol.42 , pp. 354-366
    • Forti, M.1    Tesi, A.2
  • 9
    • 0033327180 scopus 로고    scopus 로고
    • Stability analysis of Hopfield-type neural network
    • Nov.
    • J. C. Juang, "Stability analysis of Hopfield-type neural network," IEEE Trans. Neural Networks, vol. 10, pp. 1366-1374, Nov. 1999.
    • (1999) IEEE Trans. Neural Networks , vol.10 , pp. 1366-1374
    • Juang, J.C.1
  • 10
    • 0028377673 scopus 로고
    • On a class of globally stable neural circuits
    • Feb.
    • E. Kaszkurewicz and A. Bhaya, "On a class of globally stable neural circuits," IEEE Trans. Circuits Syst. I, vol. 41, pp. 171-174, Feb. 1994.
    • (1994) IEEE Trans. Circuits Syst. I , vol.41 , pp. 171-174
    • Kaszkurewicz, E.1    Bhaya, A.2
  • 11
    • 0029359622 scopus 로고
    • Comments on 'Necessary and sufficient condition for absolute stability of neural networks
    • Aug.
    • _, "Comments on 'Necessary and sufficient condition for absolute stability of neural networks'," IEEE Trans. Circuits Syst. I, vol. 42, pp. 497-499, Aug. 1995.
    • (1995) IEEE Trans. Circuits Syst. I , vol.42 , pp. 497-499
  • 13
    • 0035508696 scopus 로고    scopus 로고
    • An additive diagonal-stability condition for absolute exponential stability of a general class of neural networks
    • Nov.
    • X. B. Liang and J. Wang, "An additive diagonal-stability condition for absolute exponential stability of a general class of neural networks," IEEE Trans. Circuits Syst. I, vol. 48, pp. 1308-1317, Nov. 2001.
    • (2001) IEEE Trans. Circuits Syst. I , vol.48 , pp. 1308-1317
    • Liang, X.B.1    Wang, J.2
  • 14
    • 0034243274 scopus 로고    scopus 로고
    • Absolute exponential stability of neural networks with a general class of activation functions
    • Aug.
    • _, "Absolute exponential stability of neural networks with a general class of activation functions," IEEE Trans. Circuits Syst. I, vol. 47, pp. 1258-1263, Aug. 2000.
    • (2000) IEEE Trans. Circuits Syst. I , vol.47 , pp. 1258-1263
  • 15
    • 0000662817 scopus 로고    scopus 로고
    • A comment onn equilibria, stability, and instability of Hopfield neural networks'
    • Nov.
    • X. B. Liang, "A comment onn equilibria, stability, and instability of Hopfield neural networks'," IEEE Trans. Neural Networks, vol. 11, pp. 1506-1507, Nov. 2000.
    • (2000) IEEE Trans. Neural Networks , vol.11 , pp. 1506-1507
    • Liang, X.B.1
  • 16
    • 0000810242 scopus 로고    scopus 로고
    • A proof of Kaszkurewicz and Bhaya's conjecture on absolute stability of neural networks in two-neuron case
    • Apr.
    • X. B. Liang and J. Wang, "A proof of Kaszkurewicz and Bhaya's conjecture on absolute stability of neural networks in two-neuron case," IEEE Trans. Circuits Syst. I, vol. 47, pp. 609-611, Apr. 2000.
    • (2000) IEEE Trans. Circuits Syst. I , vol.47 , pp. 609-611
    • Liang, X.B.1    Wang, J.2
  • 17
    • 0031272074 scopus 로고    scopus 로고
    • Comments on 'new conditions for global stability of neural networks with application to linear and quadratic programming problems'
    • Nov.
    • X. B. Liang and L. D. Wu, "Comments on 'new conditions for global stability of neural networks with application to linear and quadratic programming problems'," IEEE Trans. Circuits Syst. I, vol. 44, pp. 1099-1101, Nov. 1997.
    • (1997) IEEE Trans. Circuits Syst. I , vol.44 , pp. 1099-1101
    • Liang, X.B.1    Wu, L.D.2
  • 18
    • 0030189369 scopus 로고    scopus 로고
    • Necessary and sufficient conditions for absolute exponential stability of Hopfield-type neural networks
    • X. B. Liang and T. Yamaguchi, "Necessary and sufficient conditions for absolute exponential stability of Hopfield-type neural networks," IEICE Trans. Inform. Syst., vol. E79-D, pp. 990-993, 1996.
    • (1996) IEICE Trans. Inform. Syst. , vol.E79-D , pp. 990-993
    • Liang, X.B.1    Yamaguchi, T.2
  • 19
    • 0031200626 scopus 로고    scopus 로고
    • Necessary and sufficient conditions for absolute exponential stability of a class of nonsymmetric neural networks
    • _, "Necessary and sufficient conditions for absolute exponential stability of a class of nonsymmetric neural networks," IEICE Trans. Inform. Syst., vol. E80-D, pp. 802-807, 1997.
    • (1997) IEICE Trans. Inform. Syst. , vol.E80-D , pp. 802-807
  • 20
    • 0032069434 scopus 로고    scopus 로고
    • New sufficient conditions for absolute stability of neural networks
    • May
    • X. B. Liang and L. D. Wu, "New sufficient conditions for absolute stability of neural networks," IEEE Trans. Circuits Syst. I, vol. 45, pp. 584-586, May 1998.
    • (1998) IEEE Trans. Circuits Syst. I , vol.45 , pp. 584-586
    • Liang, X.B.1    Wu, L.D.2
  • 21
    • 0025749653 scopus 로고
    • Exponential stability and a systematic synthesis of a neural network for quadratic minimization
    • S. I. Sudharsanan and M. K. Sundareshan, "Exponential stability and a systematic synthesis of a neural network for quadratic minimization," Neural Networks, vol. 4, pp. 599-613, 1991.
    • (1991) Neural Networks , vol.4 , pp. 599-613
    • Sudharsanan, S.I.1    Sundareshan, M.K.2
  • 22
    • 0032643732 scopus 로고    scopus 로고
    • Global exponential stability of a class of neural circuits
    • June
    • X. B. Liang and L. D. Wu, "Global exponential stability of a class of neural circuits," IEEE Trans. Circuits Syst. I, vol. 46, pp. 748-751, June 1999.
    • (1999) IEEE Trans. Circuits Syst. I , vol.46 , pp. 748-751
    • Liang, X.B.1    Wu, L.D.2
  • 23
    • 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. B. 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 Networks, vol. 12, pp. 349-359, Mar. 2001.
    • (2001) IEEE Trans. Neural Networks , vol.12 , pp. 349-359
    • Liang, X.B.1    Si, J.2
  • 24
    • 0033332523 scopus 로고    scopus 로고
    • Estimate of exponential convergence rate and exponential stability for neural networks
    • Nov.
    • Y. Zhang, P. A. Heng, and A. W. C. Fu, "Estimate of exponential convergence rate and exponential stability for neural networks," IEEE Trans. Neural Networks, vol. 10, pp. 1487-1493, Nov. 1999.
    • (1999) IEEE Trans. Neural Networks , vol.10 , pp. 1487-1493
    • Zhang, Y.1    Heng, P.A.2    Fu, A.W.C.3
  • 25
    • 0035307304 scopus 로고    scopus 로고
    • Global asymptotic and exponential stability of a dynamic neural system with asymmetric connection weight weights
    • Apr.
    • Y. Xia and J. Wang, "Global asymptotic and exponential stability of a dynamic neural system with asymmetric connection weight weights," IEEE Trans. Automat. Contr., vol. 46, pp. 635-638, Apr. 2001.
    • (2001) IEEE Trans. Automat. Contr. , vol.46 , pp. 635-638
    • Xia, Y.1    Wang, J.2
  • 26
    • 0035272372 scopus 로고    scopus 로고
    • Nonlinear measures: A new approach to exponential stability analysis for Hopfield-type neural networks
    • Mar.
    • H. Qiao, J. G. Peng, and Z. B. Xu, "Nonlinear measures: a new approach to exponential stability analysis for Hopfield-type neural networks," IEEE Trans. Neural Networks, vol. 12, pp. 360-370, Mar. 2001.
    • (2001) IEEE Trans. Neural Networks , vol.12 , pp. 360-370
    • Qiao, H.1    Peng, J.G.2    Xu, Z.B.3
  • 27
    • 84977698537 scopus 로고
    • Some theorems on properties of dc equations of nonlinear networks
    • I. W. Sandberg and A. N. Wilson Jr., "Some theorems on properties of dc equations of nonlinear networks," Bell Syst. Tech. J., vol. 48, no. 1, pp. 1-34, 1969.
    • (1969) Bell Syst. Tech. J. , vol.48 , Issue.1 , pp. 1-34
    • Sandberg, I.W.1    Wilson A.N., Jr.2
  • 28
    • 0001326068 scopus 로고
    • Some generalizations of positive definiteness and monotonicity
    • M. Fiedler and V. Ptak, "Some generalizations of positive definiteness and monotonicity," Numer. Math., vol. 9, no. 2, pp. 163-172, 1966.
    • (1966) Numer. Math. , vol.9 , Issue.2 , pp. 163-172
    • Fiedler, M.1    Ptak, V.2
  • 30
    • 38249012613 scopus 로고
    • Recent directions in matrix stability
    • D. Hershkowitz,"Recent directions in matrix stability," Linear Algebra Applicat., vol. 172, pp. 161-186, 1992.
    • (1992) Linear Algebra Applicat. , vol.172 , pp. 161-186
    • Hershkowitz, D.1
  • 32
    • 0030273368 scopus 로고    scopus 로고
    • Dynamics of a winner-take-all neural network
    • Y. G. Fang, M. A. Cohen, and T. G. Kincaid, "Dynamics of a winner-take-all neural network," Neural Networks, vol. 92, pp. 1141-1154, 1996.
    • (1996) Neural Networks , vol.92 , pp. 1141-1154
    • Fang, Y.G.1    Cohen, M.A.2    Kincaid, T.G.3
  • 33
    • 0024909476 scopus 로고
    • Convergent activation dynamics in continuous time networks
    • M. W. Hirsch, "Convergent activation dynamics in continuous time networks," Neural Networks, vol. 2, pp. 331-349, 1989.
    • (1989) Neural Networks , vol.2 , pp. 331-349
    • Hirsch, M.W.1
  • 34
    • 0013317737 scopus 로고    scopus 로고
    • On the existence and uniqueness of equilibrium for neural networks with continuous and monotonically increasing activation functions
    • submitted for publication
    • X. B. Liang, "On the existence and uniqueness of equilibrium for neural networks with continuous and monotonically increasing activation functions," IEEE Trans. Neural Networks, submitted for publication.
    • IEEE Trans. Neural Networks
    • Liang, X.B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.