Passivity Analysis of Stochastic Neural Networks With Multiple Time Delays
This paper deals with the problem of passivity
analysis for stochastic neural networks with leakage, discrete and
distributed delays. By using delay partitioning technique, free
weighting matrix method and stochastic analysis technique, several
sufficient conditions for the passivity of the addressed neural
networks are established in terms of linear matrix inequalities
(LMIs), in which both the time-delay and its time derivative can be
fully considered. A numerical example is given to show the
usefulness and effectiveness of the obtained results.
[1] M. Galicki, H. Witte, J.D¨orschel, M. Eiselt, G. Griessbach, Common
optimization of adaptive preprocessing units and a neural network during
learning period. Application in EEG pattern recognition, Neural Networks
10 (1997) 1153-1163.
[2] D. Zhou, J. Cao, Globally exponential stability conditions for cellular
neural networks with time-varying delays, Appl. Math. Comput. 131
(2002) 487-496.
[3] J. Cao, J. Wang, Global asymptotic and robust stability of recurrent neural
networks with time delays, IEEE Trans. Circuits Syst. I, Reg. Papers, 52
(2) (2005) 417-426.
[4] Z. Wu, P. Shi, H. Su, J. Chu, Passivity analysis for discrete-time stochastic
Markovian jump neural networks with mixed time delays, IEEE Trans.
Neural Netw. 22 (2011) 1566-1575.
[5] A. Rawat, R.N. Yadav, S.C. Shrivastava, Neural network applications in
smart antenna arrays: a review, Int. J. Electron. Commun. (AE¨U ) 66
(2012) 903-912.
[6] H. Huang, G. Feng, Delay-dependent stability for uncertain stochastic
neural networks with time-varying delay, Physica A 381 (15) (2007)
93C103.
[7] J. Zhang, P. Shi, J. Qiu, Novel robust stability criteria for uncertain
stochastic Hopfield neural networks with time-varying delays, Nonlinear
Anal. Real World Appl. 8 (4) (2007) 1349-1357.
[8] W. Chen, X. Lu, Mean square exponential stability of uncertain stochastic
delayed neural networks, Phys. Lett. A. 372 (7) (2008) 1061-1069.
[9] H. Zhang, Y. Wang, Stability analysis of Markovian jumping stochastic
CohenCGrossberg neural networks with mixed time delays, IEEE Trans.
Neural Netw. 19 (2) (2008) 366-370.
[10] W. Yu, Passivity analysis for dynamic multilayer neuro identifier, IEEE
Trans. Circuits Syst. I 50 (1) (2003) 173-178.
[11] H. Li, H. Gao, P. Shi, New passivity analysis for neural networks with
discrete and distributed delays, IEEE Trans, Neural Netw. 21 (11) (2010)
1842-1847.
[12] R. Sakthivel, A. Arunkumar, K. Mathiyalagan, S. Marshal Anthoni,
Robust passivity analysis of fuzzy Cohen-Grossberg BAM neural
networks with time-varying delays, Appl. Math. Comput. 218 (7) (2011)
3799-3809.
[13] P. Balasubramaniam, G. Nagamani, R. Rakkiyappan, Passivity analysis
for neural networks of neutral type with Markovian jumping parameters
and time delay in the leakage term. Commun. Nonlinear SCI. Numer.
Simulat. 16 (2011) 4422-4437.
[14] Q. Song, J. Liang, Z. Wang, Passivity analysis of discrete-time stochastic
neural networks with time-varying delays, Neurocomputing 72 (7) (2009)
1782-1788.
[15] H. Li, C. Wang, P. Shi, New passivity results for uncertain discrete-time
stochastic neural networks with mixed time delays, Neurocomputing 73
(16) (2010) 3291-3299.
[16] J. Fu, H. Zhang, T. Ma, On passivity analysis for stochastic neural
networks with interval time-varying delay, Neurocomputing 73 (4) (2010)
795-801.
[17] Y. Chen, H. Wang, A. Xue, Passivity analysis of stochastic time-delay
neural networks, Nonlinear Dynam. 61 (1-2) (2010) 71-82.
[18] K. Mathiyalagan, R. Sakthivel, S. Marshal Anthoni, New robust passivity
criteria for stochastic fuzzy BAM neural networks with time-varying
delays, Commun. Nonlinear SCI. Numer. Simulat. 17 (3) (2012) 1392-
1407.
[19] P. Balasubramaniam, G. Nagamani, Global robust passivity analysis for
stochastic interval neural networks with interval time-varying delays and
Markovian jumping parameters, J. Optim. Theory Appl. 149 (1) (2011)
197-215.
[20] P. Balasubramaniam, G. Nagamani, Global robust passivity analysis for
stochastic fuzzy interval neural networks with time-varying delays, Expert
Syst. Appl. 39 (1) (2012) 732-742.
[21] X. Chen, W.X. Zheng, Stochastic state estimation for neural networks
with distributed delays and Markovian jump, Neural Netw. 25 (2012)
14-20.
[22] Z. Zhao, Q. Song, S. He, Passivity analysis of stochastic neural networks
with time-varying delays and leakage delay, Neurocomputing 125 (2014)
22-27.
[23] Z. Wang, H. Shu, Y. Liu, DWC. Ho, X. Liu, Robust stability analysis
of generalized neural networks with discrete and distributed time delays,
Chaos Solitons Fract 30 (4) (2006) 886-896.
[24] T. Li, X. Yang, P. Yang, S. Fei, New delay-variation-dependent stability
for neural networks with time-varying delay, Neurocomputing 101 (2013)
361-169.
[1] M. Galicki, H. Witte, J.D¨orschel, M. Eiselt, G. Griessbach, Common
optimization of adaptive preprocessing units and a neural network during
learning period. Application in EEG pattern recognition, Neural Networks
10 (1997) 1153-1163.
[2] D. Zhou, J. Cao, Globally exponential stability conditions for cellular
neural networks with time-varying delays, Appl. Math. Comput. 131
(2002) 487-496.
[3] J. Cao, J. Wang, Global asymptotic and robust stability of recurrent neural
networks with time delays, IEEE Trans. Circuits Syst. I, Reg. Papers, 52
(2) (2005) 417-426.
[4] Z. Wu, P. Shi, H. Su, J. Chu, Passivity analysis for discrete-time stochastic
Markovian jump neural networks with mixed time delays, IEEE Trans.
Neural Netw. 22 (2011) 1566-1575.
[5] A. Rawat, R.N. Yadav, S.C. Shrivastava, Neural network applications in
smart antenna arrays: a review, Int. J. Electron. Commun. (AE¨U ) 66
(2012) 903-912.
[6] H. Huang, G. Feng, Delay-dependent stability for uncertain stochastic
neural networks with time-varying delay, Physica A 381 (15) (2007)
93C103.
[7] J. Zhang, P. Shi, J. Qiu, Novel robust stability criteria for uncertain
stochastic Hopfield neural networks with time-varying delays, Nonlinear
Anal. Real World Appl. 8 (4) (2007) 1349-1357.
[8] W. Chen, X. Lu, Mean square exponential stability of uncertain stochastic
delayed neural networks, Phys. Lett. A. 372 (7) (2008) 1061-1069.
[9] H. Zhang, Y. Wang, Stability analysis of Markovian jumping stochastic
CohenCGrossberg neural networks with mixed time delays, IEEE Trans.
Neural Netw. 19 (2) (2008) 366-370.
[10] W. Yu, Passivity analysis for dynamic multilayer neuro identifier, IEEE
Trans. Circuits Syst. I 50 (1) (2003) 173-178.
[11] H. Li, H. Gao, P. Shi, New passivity analysis for neural networks with
discrete and distributed delays, IEEE Trans, Neural Netw. 21 (11) (2010)
1842-1847.
[12] R. Sakthivel, A. Arunkumar, K. Mathiyalagan, S. Marshal Anthoni,
Robust passivity analysis of fuzzy Cohen-Grossberg BAM neural
networks with time-varying delays, Appl. Math. Comput. 218 (7) (2011)
3799-3809.
[13] P. Balasubramaniam, G. Nagamani, R. Rakkiyappan, Passivity analysis
for neural networks of neutral type with Markovian jumping parameters
and time delay in the leakage term. Commun. Nonlinear SCI. Numer.
Simulat. 16 (2011) 4422-4437.
[14] Q. Song, J. Liang, Z. Wang, Passivity analysis of discrete-time stochastic
neural networks with time-varying delays, Neurocomputing 72 (7) (2009)
1782-1788.
[15] H. Li, C. Wang, P. Shi, New passivity results for uncertain discrete-time
stochastic neural networks with mixed time delays, Neurocomputing 73
(16) (2010) 3291-3299.
[16] J. Fu, H. Zhang, T. Ma, On passivity analysis for stochastic neural
networks with interval time-varying delay, Neurocomputing 73 (4) (2010)
795-801.
[17] Y. Chen, H. Wang, A. Xue, Passivity analysis of stochastic time-delay
neural networks, Nonlinear Dynam. 61 (1-2) (2010) 71-82.
[18] K. Mathiyalagan, R. Sakthivel, S. Marshal Anthoni, New robust passivity
criteria for stochastic fuzzy BAM neural networks with time-varying
delays, Commun. Nonlinear SCI. Numer. Simulat. 17 (3) (2012) 1392-
1407.
[19] P. Balasubramaniam, G. Nagamani, Global robust passivity analysis for
stochastic interval neural networks with interval time-varying delays and
Markovian jumping parameters, J. Optim. Theory Appl. 149 (1) (2011)
197-215.
[20] P. Balasubramaniam, G. Nagamani, Global robust passivity analysis for
stochastic fuzzy interval neural networks with time-varying delays, Expert
Syst. Appl. 39 (1) (2012) 732-742.
[21] X. Chen, W.X. Zheng, Stochastic state estimation for neural networks
with distributed delays and Markovian jump, Neural Netw. 25 (2012)
14-20.
[22] Z. Zhao, Q. Song, S. He, Passivity analysis of stochastic neural networks
with time-varying delays and leakage delay, Neurocomputing 125 (2014)
22-27.
[23] Z. Wang, H. Shu, Y. Liu, DWC. Ho, X. Liu, Robust stability analysis
of generalized neural networks with discrete and distributed time delays,
Chaos Solitons Fract 30 (4) (2006) 886-896.
[24] T. Li, X. Yang, P. Yang, S. Fei, New delay-variation-dependent stability
for neural networks with time-varying delay, Neurocomputing 101 (2013)
361-169.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:68156", author = "Biao Qin and Jin Huang and Jiaojiao Ren and Wei Kang", title = "Passivity Analysis of Stochastic Neural Networks With Multiple Time Delays", abstract = "This paper deals with the problem of passivity
analysis for stochastic neural networks with leakage, discrete and
distributed delays. By using delay partitioning technique, free
weighting matrix method and stochastic analysis technique, several
sufficient conditions for the passivity of the addressed neural
networks are established in terms of linear matrix inequalities
(LMIs), in which both the time-delay and its time derivative can be
fully considered. A numerical example is given to show the
usefulness and effectiveness of the obtained results.
", keywords = "Passivity, Stochastic neural networks, Multiple time
delays, Linear matrix inequalities (LMIs).", volume = "8", number = "8", pages = "1153-7", }
