An Analysis of Global Stability of a Class of Neutral-Type Neural Systems with Time Delays
This paper derives some new sufficient conditions for
the stability of a class of neutral-type neural networks with discrete
time delays by employing a suitable Lyapunov functional. The
obtained conditions can be easily verified as they can be expressed
in terms of the network parameters only. It is shown that the results
presented in this paper for neutral-type delayed neural networks establish
a new set of stability criteria, and therefore can be considered
as the alternative results to the previously published literature results.
A numerical example is also given to demonstrate the applicability
of our proposed stability criterion.
[1] M. Cohen and S. Grossberg, "Absolute stability of global pattern formation
and parallel memory storage by competitive neural networks", IEEE
Transactions Systems, Man and Cybernetics, vol. 13, no. 5, pp. 815-826,
September-October 1983.
[2] L. Wang and X. Zou, "Exponentially stability of Cohen-Grossberg neural
networks", Neural Networks, vol. 15, no. 3, pp. 415-422, April 2002.
[3] S. Mohamad and K. Gopalsamy, "Exponential stability of continuoustime
and discrete-time cellular neural networks with delays", Applied
Mathematics and Computation., vol. 135, no. 1, pp. 17-38, February 2003.
[4] J. J. Hopfield, "Neural networks and physical systems with emergent
collective computational abilities", Proc. Nat. Acad. Sci. USA., vol. 79,
no. 8, pp. 2554-2558, April 1982.
[5] L. O. Chua and L. Yang, "Cellular Neural Networks : Theory", IEEE
Transactions on Circuits and Syststems-I, vol. 35, no. 10, pp. 1257-1272,
October 1988.
[6] J. Cao, "Global stability conditions for delay CNNs", IEEE Transactions
on Circuits and Syststems-I, vol. 48, no. 11, pp. 1330-1333, November
2001.
[7] S. Arik, "Stability analysis of delayed neural networks", IEEE Transactions
on Circuits and Syststems-I, vol. 47, no. 7, pp. 1089-1092, July
2000.
[8] P. Baldi and A. F. Atiya, "How delays affect neural dynamics and
learning", IEEE Trans. Neural Networks., vol. 5, no. 4, pp. 612-621,
July 1994.
[9] Z. Wang, J. Lam and K. J. Burnham, "Stability analysis and observer
design for neutral delay systems", IEEE Transactions on Automatic
Control, vol. 47, no. 3, pp. 478-483, March 2002.
[10] L. Wang and X. Zou, "Harmless delays in Cohen-Grossberg neural
networks", Physica D, vol. 170, no. 2, pp. 162-173, September 2002.
[11] S. Xu, J. Lam, W. C. Ho, and Y. Zou, "Delay-dependent exponential
stability for a class of neural networks with time delays", Journal
of Computational Applied Mathematics, vol. 183, no. 1, pp. 16-28,
November 2005.
[12] S. Arik and V. Tavsanoglu, "On the global asymptotic stability of
delayed cellular neural networks," IEEE Transactions on Circuits and
Syststems-I, vol. 47, no 4, pp. 571-574, April 2000.
[13] C. H. Lien, "Asymptotic criterion for neutral systems with multiple time
delays", Electron Letters, vol. 35, no. 10, pp. 850-852, May. 1999.
[14] R. P. Agarwal and S. R. Grace, "Asymptotic stability of differential
systems of neutral type", Appl. Math. Lett., vol. 13, no. 8, pp. 15-19,
November 2000.
[15] Ju H. Park, C.H. Park, O.M. Kwon and S.M. Lee, "A new stability
criterion for bidirectional associative memory neural networks of neutraltype,"
Applied Mathematics and Computation, vol. 199, no: 2, pp. 716-
722, June 2008.
[16] Ju H. Park, O.M. Kwon and S.M. Lee, "LMI optimization approach on
stability for delayed neural networks of neutral-type," Applied Mathematics
and Computation, vol. 196, no : 1, pp. 236-244, February 2008.
[17] R. Rakkiyappan and P. Balasubramaniam, "New global exponential
stability results for neutral type neural networks with distributed time
delays," Neurocomputing, vol. 71, no : 4-6, pp.1039-1045, January 2008.
[18] K.W. Yu and C.H. Lien "Stability criteria for uncertain neutral systems
with interval time-varying delays," Chaos, Solitons and Fractals, vol. 38,
no : 3, pp.650-657, November 2008.
[19] J. Zhang, P, Shi and J. Qiu, "Robust stability criteria for uncertain neutral
system with time delay and nonlinear uncertainties," Chaos, Solitons and
Fractals, vol. 38, no : 1, pp. 160-167, October 2008.
[20] Y. Chen, A. Xue, R. Lu and S. Zhou, "On robustly exponential stability
of uncertain neutral systems with time-varying delays and nonlinear
perturbations," Nonlinear Analysis: Theory, Methods and Applications,
vol. 68, no : 8, pp. 2464-2470, April 2008.
[21] B. Wang, X. Liu and S. Zhong, "New stability analysis for uncertain
neutral system with time-varying delay," Applied Mathematics and Computation,
vol. 197, no : 1, pp.457-465, March 2008.
[22] W.A. Zhang and L. Yu, "Delay-dependent Robust Stability of Neutral
Systems with Mixed Delays and Nonlinear Perturbations," Acta Automatica
Sinica, vol. 33, no : 8, pp.863-866, August 2007.
[23] J. Cao, S. Zhong and Y. Hu, "Global stability analysis for a class
of neural networks with varying delays and control input," Applied
Mathematics and Computation, vol. 189, no : 2, pp.1480-1490, June 2007.
[24] W. Xiong and J. Liang, "Novel stability criteria for neutral systems
with multiple time delays," Chaos, Solitons and Fractals, vol. 32, no : 5,
pp.1735-1741, June 2007.
[25] X.G. Liu, M. Wu, R. Martin and M.L. Tang, "Delay-dependent stability
analysis for uncertain neutral systems with time-varying delays," Mathematics
and Computers in Simulation, vol. 75, no : 1-2, pp.15-27, May
2007.
[26] H. Li, S.M. Zhong and H.B. Li, "Some new simple stability criteria of
linear neutral systems with a single delay," Journal of Computational and
Applied Mathematics, vol. 200, no : 1, pp.441-447, March 2007.
[27] W.H. Chen and W.X. Zheng, "Delay-dependent robust stabilization for
uncertain neutral systems with distributed delays," Automatica, vol. 43,
no : 1, pp.95-104, January 2007.
[28] C.J. Cheng, T. L. Liao, J.J. Yan and C. C. Hwang, "Globally Asymptotic
Stability of a Class of Neutral-Type Neural Networks With Delays," IEEE
Transactions on Systems Man and Cybernetics- Part B, vol. 6, no. 5, pp.
1191- 1195, October 2006.
[1] M. Cohen and S. Grossberg, "Absolute stability of global pattern formation
and parallel memory storage by competitive neural networks", IEEE
Transactions Systems, Man and Cybernetics, vol. 13, no. 5, pp. 815-826,
September-October 1983.
[2] L. Wang and X. Zou, "Exponentially stability of Cohen-Grossberg neural
networks", Neural Networks, vol. 15, no. 3, pp. 415-422, April 2002.
[3] S. Mohamad and K. Gopalsamy, "Exponential stability of continuoustime
and discrete-time cellular neural networks with delays", Applied
Mathematics and Computation., vol. 135, no. 1, pp. 17-38, February 2003.
[4] J. J. Hopfield, "Neural networks and physical systems with emergent
collective computational abilities", Proc. Nat. Acad. Sci. USA., vol. 79,
no. 8, pp. 2554-2558, April 1982.
[5] L. O. Chua and L. Yang, "Cellular Neural Networks : Theory", IEEE
Transactions on Circuits and Syststems-I, vol. 35, no. 10, pp. 1257-1272,
October 1988.
[6] J. Cao, "Global stability conditions for delay CNNs", IEEE Transactions
on Circuits and Syststems-I, vol. 48, no. 11, pp. 1330-1333, November
2001.
[7] S. Arik, "Stability analysis of delayed neural networks", IEEE Transactions
on Circuits and Syststems-I, vol. 47, no. 7, pp. 1089-1092, July
2000.
[8] P. Baldi and A. F. Atiya, "How delays affect neural dynamics and
learning", IEEE Trans. Neural Networks., vol. 5, no. 4, pp. 612-621,
July 1994.
[9] Z. Wang, J. Lam and K. J. Burnham, "Stability analysis and observer
design for neutral delay systems", IEEE Transactions on Automatic
Control, vol. 47, no. 3, pp. 478-483, March 2002.
[10] L. Wang and X. Zou, "Harmless delays in Cohen-Grossberg neural
networks", Physica D, vol. 170, no. 2, pp. 162-173, September 2002.
[11] S. Xu, J. Lam, W. C. Ho, and Y. Zou, "Delay-dependent exponential
stability for a class of neural networks with time delays", Journal
of Computational Applied Mathematics, vol. 183, no. 1, pp. 16-28,
November 2005.
[12] S. Arik and V. Tavsanoglu, "On the global asymptotic stability of
delayed cellular neural networks," IEEE Transactions on Circuits and
Syststems-I, vol. 47, no 4, pp. 571-574, April 2000.
[13] C. H. Lien, "Asymptotic criterion for neutral systems with multiple time
delays", Electron Letters, vol. 35, no. 10, pp. 850-852, May. 1999.
[14] R. P. Agarwal and S. R. Grace, "Asymptotic stability of differential
systems of neutral type", Appl. Math. Lett., vol. 13, no. 8, pp. 15-19,
November 2000.
[15] Ju H. Park, C.H. Park, O.M. Kwon and S.M. Lee, "A new stability
criterion for bidirectional associative memory neural networks of neutraltype,"
Applied Mathematics and Computation, vol. 199, no: 2, pp. 716-
722, June 2008.
[16] Ju H. Park, O.M. Kwon and S.M. Lee, "LMI optimization approach on
stability for delayed neural networks of neutral-type," Applied Mathematics
and Computation, vol. 196, no : 1, pp. 236-244, February 2008.
[17] R. Rakkiyappan and P. Balasubramaniam, "New global exponential
stability results for neutral type neural networks with distributed time
delays," Neurocomputing, vol. 71, no : 4-6, pp.1039-1045, January 2008.
[18] K.W. Yu and C.H. Lien "Stability criteria for uncertain neutral systems
with interval time-varying delays," Chaos, Solitons and Fractals, vol. 38,
no : 3, pp.650-657, November 2008.
[19] J. Zhang, P, Shi and J. Qiu, "Robust stability criteria for uncertain neutral
system with time delay and nonlinear uncertainties," Chaos, Solitons and
Fractals, vol. 38, no : 1, pp. 160-167, October 2008.
[20] Y. Chen, A. Xue, R. Lu and S. Zhou, "On robustly exponential stability
of uncertain neutral systems with time-varying delays and nonlinear
perturbations," Nonlinear Analysis: Theory, Methods and Applications,
vol. 68, no : 8, pp. 2464-2470, April 2008.
[21] B. Wang, X. Liu and S. Zhong, "New stability analysis for uncertain
neutral system with time-varying delay," Applied Mathematics and Computation,
vol. 197, no : 1, pp.457-465, March 2008.
[22] W.A. Zhang and L. Yu, "Delay-dependent Robust Stability of Neutral
Systems with Mixed Delays and Nonlinear Perturbations," Acta Automatica
Sinica, vol. 33, no : 8, pp.863-866, August 2007.
[23] J. Cao, S. Zhong and Y. Hu, "Global stability analysis for a class
of neural networks with varying delays and control input," Applied
Mathematics and Computation, vol. 189, no : 2, pp.1480-1490, June 2007.
[24] W. Xiong and J. Liang, "Novel stability criteria for neutral systems
with multiple time delays," Chaos, Solitons and Fractals, vol. 32, no : 5,
pp.1735-1741, June 2007.
[25] X.G. Liu, M. Wu, R. Martin and M.L. Tang, "Delay-dependent stability
analysis for uncertain neutral systems with time-varying delays," Mathematics
and Computers in Simulation, vol. 75, no : 1-2, pp.15-27, May
2007.
[26] H. Li, S.M. Zhong and H.B. Li, "Some new simple stability criteria of
linear neutral systems with a single delay," Journal of Computational and
Applied Mathematics, vol. 200, no : 1, pp.441-447, March 2007.
[27] W.H. Chen and W.X. Zheng, "Delay-dependent robust stabilization for
uncertain neutral systems with distributed delays," Automatica, vol. 43,
no : 1, pp.95-104, January 2007.
[28] C.J. Cheng, T. L. Liao, J.J. Yan and C. C. Hwang, "Globally Asymptotic
Stability of a Class of Neutral-Type Neural Networks With Delays," IEEE
Transactions on Systems Man and Cybernetics- Part B, vol. 6, no. 5, pp.
1191- 1195, October 2006.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:62631", author = "Ozlem Faydasicok and Sabri Arik", title = "An Analysis of Global Stability of a Class of Neutral-Type Neural Systems with Time Delays", abstract = "This paper derives some new sufficient conditions for
the stability of a class of neutral-type neural networks with discrete
time delays by employing a suitable Lyapunov functional. The
obtained conditions can be easily verified as they can be expressed
in terms of the network parameters only. It is shown that the results
presented in this paper for neutral-type delayed neural networks establish
a new set of stability criteria, and therefore can be considered
as the alternative results to the previously published literature results.
A numerical example is also given to demonstrate the applicability
of our proposed stability criterion.", keywords = "Stability Analysis, Neutral-Type Neural Networks,
Time Delay Systems, Lyapunov Functionals.", volume = "6", number = "4", pages = "477-5", }
