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Volumn 17, Issue 3, 2004, Pages 379-390

Absolute exponential stability of recurrent neural networks with Lipschitz-continuous activation functions and time delays

Author keywords

Absolute exponential stability; Additive diagonal stability; Delay Halanay type inequality; Delayed neural networks; Partial Lipschitz continuity

Indexed keywords

FUNCTIONS; LYAPUNOV METHODS; OPTIMIZATION; SYSTEM STABILITY;

EID: 1642287604     PISSN: 08936080     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.neunet.2003.08.007     Document Type: Article
Times cited : (224)

References (36)
  • 1
    • 0032070578 scopus 로고    scopus 로고
    • A comment on Comments on necessary and sufficient condition for absolute stability of neural networks
    • Arik S., Tavsanoglu V. A comment on Comments on necessary and sufficient condition for absolute stability of neural networks. IEEE Trans Circuits Syst. I. 45:1998;595-596.
    • (1998) IEEE Trans Circuits Syst. I , vol.45 , pp. 595-596
    • Arik, S.1    Tavsanoglu, V.2
  • 3
    • 0030081051 scopus 로고    scopus 로고
    • Frustration, stability and delayed-induced oscillations in a neural network model
    • Belair J., Campbell S.A., Driessche P.V.D. Frustration, stability and delayed-induced oscillations in a neural network model. SIAM J. Appl. Math. 56:1996;245-255.
    • (1996) SIAM J. Appl. Math. , vol.56 , pp. 245-255
    • Belair, J.1    Campbell, S.A.2    Driessche, P.V.D.3
  • 4
    • 0027555144 scopus 로고
    • Neural network for quadratic optimization with bound constraints
    • Bouzerman A., Pattison T.R. Neural network for quadratic optimization with bound constraints. IEEE Trans Neural Networks. 4:1993;293-303.
    • (1993) IEEE Trans Neural Networks , vol.4 , pp. 293-303
    • Bouzerman, A.1    Pattison, T.R.2
  • 6
    • 0032589602 scopus 로고    scopus 로고
    • Global stability analysis in delayed cellular neural networks
    • Cao J. Global stability analysis in delayed cellular neural networks. Physical Review E. 59:1999;5940-5944.
    • (1999) Physical Review e , vol.59 , pp. 5940-5944
    • Cao, J.1
  • 7
    • 0034729056 scopus 로고    scopus 로고
    • Periodic oscillation and exponential stability of delayed CNNs
    • Cao J. Periodic oscillation and exponential stability of delayed CNNs. Physics Letters A. 270:2000;157-163.
    • (2000) Physics Letters a , vol.270 , pp. 157-163
    • Cao, J.1
  • 8
    • 0035303488 scopus 로고    scopus 로고
    • A set of stability criteria for delayed cellular neural networks
    • Cao J. A set of stability criteria for delayed cellular neural networks. IEEE Trans Circuits Syst. I. 48:2001;494-498.
    • (2001) IEEE Trans Circuits Syst. I , vol.48 , pp. 494-498
    • Cao, J.1
  • 9
    • 0035507277 scopus 로고    scopus 로고
    • Global stability conditions for delayed CNNs
    • Cao J. Global stability conditions for delayed CNNs. IEEE Trans Circuits Syst. I. 48:2001;1330-1333.
    • (2001) IEEE Trans Circuits Syst. I , vol.48 , pp. 1330-1333
    • Cao, J.1
  • 10
    • 0034369985 scopus 로고    scopus 로고
    • On the exponential stability and periodic solution of delayed cellular neural networks
    • Cao J., Li Q. On the exponential stability and periodic solution of delayed cellular neural networks. Journal of Mathematical Analysis and Applications. 252:2000;50-64.
    • (2000) Journal of Mathematical Analysis and Applications , vol.252 , pp. 50-64
    • Cao, J.1    Li, Q.2
  • 11
    • 0034136641 scopus 로고    scopus 로고
    • Periodic oscillatory solution of bidirectional associative memory networks with delays
    • Cao J., Wang L. Periodic oscillatory solution of bidirectional associative memory networks with delays. Physical Review E. 61:2000;1825-1828.
    • (2000) Physical Review e , vol.61 , pp. 1825-1828
    • Cao, J.1    Wang, L.2
  • 12
    • 0032418487 scopus 로고    scopus 로고
    • Stability analysis of delayed cellular neural networks
    • Cao J., Zhou D. Stability analysis of delayed cellular neural networks. Neural Networks. 11:1998;1601-1605.
    • (1998) Neural Networks , vol.11 , pp. 1601-1605
    • Cao, J.1    Zhou, D.2
  • 13
    • 0017418017 scopus 로고
    • On the application of degree theory to the analysis of resistive nonlinear networks
    • Chua L.O., Wang N.N. On the application of degree theory to the analysis of resistive nonlinear networks. Int. J. Circuit Theory Applicat. 5:1977;45-68.
    • (1977) Int. J. Circuit Theory Applicat. , vol.5 , pp. 45-68
    • Chua, L.O.1    Wang, N.N.2
  • 15
    • 0001326068 scopus 로고
    • Some generalizations of positive definiteness and monotonicity
    • Fiedler M., Pták V. Some generalizations of positive definiteness and monotonicity. Numer. Math. 9:1966;163-172.
    • (1966) Numer. Math. , vol.9 , pp. 163-172
    • Fiedler, M.1    Pták, V.2
  • 16
    • 0030169001 scopus 로고    scopus 로고
    • A note on neural networks with multiple equilibrium points
    • Forti M. A note on neural networks with multiple equilibrium points. IEEE Trans Circuits Syst. I. 43:1996;487-491.
    • (1996) IEEE Trans Circuits Syst. I , vol.43 , pp. 487-491
    • Forti, M.1
  • 17
    • 0028465673 scopus 로고
    • Necessary and sufficient condition for absolute stability of neural networks
    • Forti M., Manetti S., Marini M. Necessary and sufficient condition for absolute stability of neural networks. IEEE Trans Circuits Syst. I. 41:1994;491-494.
    • (1994) IEEE Trans Circuits Syst. I , vol.41 , pp. 491-494
    • Forti, M.1    Manetti, S.2    Marini, M.3
  • 19
    • 0029345226 scopus 로고
    • New conditions for global stability of neural networks with application to linear and quadratic programming problems
    • Forti M., Tesi A. New conditions for global stability of neural networks with application to linear and quadratic programming problems. IEEE Trans Circuits Syst. I. 42:1995;354-366.
    • (1995) IEEE Trans Circuits Syst. I , vol.42 , pp. 354-366
    • Forti, M.1    Tesi, A.2
  • 21
    • 0029359622 scopus 로고
    • Comments on Necessary and sufficient condition for absolute stability of neural networks
    • Kaszkurewicz E., Bhaya A. Comments on Necessary and sufficient condition for absolute stability of neural networks. IEEE Trans Circuits Syst. I. 42:1995;497-499.
    • (1995) IEEE Trans Circuits Syst. I , vol.42 , pp. 497-499
    • Kaszkurewicz, E.1    Bhaya, A.2
  • 22
    • 0000810242 scopus 로고    scopus 로고
    • A proof of Kaszkurewicz and Bhaya's conjecture on absolute stability of neural networks in two-neuron case
    • Liang X.B., Wang J. A proof of Kaszkurewicz and Bhaya's conjecture on absolute stability of neural networks in two-neuron case. IEEE Trans Circuits Syst. I. 47:2000;609-611.
    • (2000) IEEE Trans Circuits Syst. I , vol.47 , pp. 609-611
    • Liang, X.B.1    Wang, J.2
  • 23
    • 0034243274 scopus 로고    scopus 로고
    • Absolute exponential stability of neural networks with a general class of activation functions
    • Liang X.B., Wang J. Absolute exponential stability of neural networks with a general class of activation functions. IEEE Trans Circuits Syst. I. 47:2000;1258-1263.
    • (2000) IEEE Trans Circuits Syst. I , vol.47 , pp. 1258-1263
    • Liang, X.B.1    Wang, J.2
  • 24
    • 0035508696 scopus 로고    scopus 로고
    • An additive diagonal stability condition for absolute exponential stability of a general class of neural networks
    • Liang X.B., Wang J. An additive diagonal stability condition for absolute exponential stability of a general class of neural networks. IEEE Trans Circuits Syst. I. 48:2001;1308-1317.
    • (2001) IEEE Trans Circuits Syst. I , vol.48 , pp. 1308-1317
    • Liang, X.B.1    Wang, J.2
  • 25
    • 0031272074 scopus 로고    scopus 로고
    • Comments on New conditions for global stability of neural networks with application to linear and quadratic programming problems
    • Liang X.B., Wu L.D. Comments on New conditions for global stability of neural networks with application to linear and quadratic programming problems. IEEE Trans Circuits Syst. I. 44:1997;1099-1101.
    • (1997) IEEE Trans Circuits Syst. I , vol.44 , pp. 1099-1101
    • Liang, X.B.1    Wu, L.D.2
  • 26
    • 0032154933 scopus 로고    scopus 로고
    • A simple proof of a necessary and sufficient condition for absolute stability of symmetric neural networks
    • Liang X.B., Wu L.D. A simple proof of a necessary and sufficient condition for absolute stability of symmetric neural networks. IEEE Trans Circuits Syst. I. 45:1998;1010-1011.
    • (1998) IEEE Trans Circuits Syst. I , vol.45 , pp. 1010-1011
    • Liang, X.B.1    Wu, L.D.2
  • 27
    • 0032072232 scopus 로고    scopus 로고
    • A comment on Comments on necessary and sufficient condition for absolute stability of neural networks
    • Liang X.B., Wu L.D. A comment on Comments on necessary and sufficient condition for absolute stability of neural networks. IEEE Trans Circuits Syst. I. 45:1998;594.
    • (1998) IEEE Trans Circuits Syst. I , vol.45 , pp. 594
    • Liang, X.B.1    Wu, L.D.2
  • 28
    • 0032643732 scopus 로고    scopus 로고
    • Global exponential stability of a class of neural circuits
    • Liang X.B., Wu L.D. Global exponential stability of a class of neural circuits. IEEE Trans Circuits Syst. I. 46:1999;748-751.
    • (1999) IEEE Trans Circuits Syst. I , vol.46 , pp. 748-751
    • Liang, X.B.1    Wu, L.D.2
  • 29
    • 0031200626 scopus 로고    scopus 로고
    • Necessary and sufficient condition for absolute exponential stability of a class of nonsymmetric neural networks
    • Liang X.B., Yamaguchi T. Necessary and sufficient condition for absolute exponential stability of a class of nonsymmetric neural networks. IEICE Trans Inf. and Syst. E80:1997;802-807.
    • (1997) IEICE Trans Inf. and Syst. , vol.80 , pp. 802-807
    • Liang, X.B.1    Yamaguchi, T.2
  • 30
    • 0030653350 scopus 로고    scopus 로고
    • On the analysis of global and absolute stability of nonlinear continuous neural networks
    • Liang X.B., Yamaguchi T. On the analysis of global and absolute stability of nonlinear continuous neural networks. IEICE Trans Fundamentals. E80-A:1997;223-229.
    • (1997) IEICE Trans Fundamentals , vol.80 , pp. 223-229
    • Liang, X.B.1    Yamaguchi, T.2
  • 31
    • 0000459678 scopus 로고    scopus 로고
    • Global stability for cellular neural networks with time delay
    • Liao T.-L., Wang F.-C. Global stability for cellular neural networks with time delay. IEEE Trans Neural Networks. 11:2000;1481-1484.
    • (2000) IEEE Trans Neural Networks , vol.11 , pp. 1481-1484
    • Liao, T.-L.1    Wang, F.-C.2
  • 32
    • 0000256610 scopus 로고
    • Stability of analog neural networks with delay
    • Marcus C.M., Westervelt R.M. Stability of analog neural networks with delay. Phys. Rev. A. 39:1989;347-359.
    • (1989) Phys. Rev. a , vol.39 , pp. 347-359
    • Marcus, C.M.1    Westervelt, R.M.2
  • 33
    • 0001082564 scopus 로고    scopus 로고
    • Bifurcations, stability, and monotonicity properties of a delayed neural network model
    • Olien L., Belair J. Bifurcations, stability, and monotonicity properties of a delayed neural network model. Physica D. 102:1997;349-363.
    • (1997) Physica D , vol.102 , pp. 349-363
    • Olien, L.1    Belair, J.2
  • 34
    • 0032052445 scopus 로고    scopus 로고
    • Effect of delay on the boundary of the basin of attraction in a system of two neurons
    • Pakdaman K., Grotta-Ragazzo C., Malta C.P., Arino O., Vibert J.-F. Effect of delay on the boundary of the basin of attraction in a system of two neurons. Neural Networks. 11:1998;509-519.
    • (1998) Neural Networks , vol.11 , pp. 509-519
    • Pakdaman, K.1    Grotta-Ragazzo, C.2    Malta, C.P.3    Arino, O.4    Vibert, J.-F.5
  • 35
    • 84977698537 scopus 로고
    • Some theorems on properties of dc equations of nonlinear networks
    • Sandberg I.W. Jr., Willson A.N. Some theorems on properties of dc equations of nonlinear networks. Bell Syst. Tech. J. 48:1969;1-34.
    • (1969) Bell Syst. Tech. J. , vol.48 , pp. 1-34
    • Sandberg Jr., I.W.1    Willson, A.N.2
  • 36
    • 0025749653 scopus 로고
    • Exponential stability and a systematic synthesis of a neural network for quadratic minimization
    • Sudharsanan S.I., Sundareshan M.K. Exponential stability and a systematic synthesis of a neural network for quadratic minimization. Neural Networks. 4:1991;599-613.
    • (1991) Neural Networks , vol.4 , pp. 599-613
    • Sudharsanan, S.I.1    Sundareshan, M.K.2


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