Passivity Analysis of Stochastic Neural Networks With Multiple Time Delays
Authors: Biao Qin, Jin Huang, Jiaojiao Ren, Wei Kang
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).
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1096513
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1707References:
[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.