Passivity Analysis of Uncertain Stochastic Neural Networks with Discrete and Distributed Time-Varying Delays

M. SYED ALI

Abstract


This paper investigates the problem of robust passivity of uncertain stochastic neural networks with discrete and distributed time-varying delays. To reflect the most dynamical behaviors of the system, both parameter uncertainties and stochastic disturbance are considered, where parameter uncertainties enter into all the system matrices, stochastic disturbances are given in the form of a Brownian motion. By utilizing the Lyapunov functional method, the Itô differential rule and matrix analysis techniques, we establish sufficient criterion such that, for all admissible parameter uncertainties and stochastic disturbances, the stochastic neural networks is robustly passive in the sense of expectation. The delay - dependent stability condition is formulated, in which the restriction of the derivative of the time-varying delay should be less than 1 is removed. The derived criteria are expressed in terms of linear matrix inequalities (LMIs) that can be easily checked by using the standard numerical software. Illustrative examples are presented to demonstrate the effectiveness and usefulness of the proposed results.

Keywords: delayed neural networks, linear matrix inequality, lyapunov functional, parameter uncertainty, passivity

Full Text:

PDF

References


S. Arik, An improved global stability result for delayed cellular neural networks, IEEE Trans. Circuits Syst. I 49 (2002) 1211-1214.

H. Bao, J. Cao, Stochastic global exponential stability for neutral-type impulsive neural networks with mixed time-delays and Markovian jumping parameters, Commun Nonlinear Sci Numer Simulat 16 (2011) 3786-3791.

V. Bevelevich, Classical Network Synthesis, Van Nostrand, New York, 1968.

B. Boyd, L. Ghoui, E. Feron , V. Balakrishnan V, Linear Matrix Inequalities in System and Control Theory, SIAM, philadephia, PA (1994).

J. Cao, J. Wang, Global exponential stability and periodicity of recurrent neural networks with time delays, IEEE Trans. Circuits Syst. I 52(5) (2005) 920 – 931.

J. Cao, K. Yuan, H. X. Li, Global asymptotic stability of recurrent neural networks with multiple discrete delays and distributed delays, IEEE Trans. Neural Netw. 17 (2006) 1646 – 1651.

L. Yang, Y. Li, Existence and exponential stability of periodic solution for stochastic Hopfield neural networks on time scales, Neurocomputing 167 (2015) 543–550.

P. Balasubramaniam, G. Nagamani, Global robust passivity analysis for stochastic fuzzy interval neural networks with time-varying delays, Expert Syst. Appl. 39(2012) 732–742.

B. Chen, H. Y. Li, C. Lin, Q. Zhou, Passivity analysis for uncertain neural networks with discrete and distributed time - varying delays, Phys. Lett. A 373 (2009) 1242 - 1248.

L. Zhou, Novel global exponential stability criteria for hybrid BAM neural networks with proportional delays Neurocomputing 161(2015) 99–106. 16

J. Fu H. Zhang, T. Ma, Q.Zhang, On passivity analysis for stochastic neural networks with interval time - varying delay Neurocomputing 73(2010)795 - 801.

P. Gahinet, A. Nemirovski, A. Laub, M. Chilali, LMI control toolbox user’s guide, Massachusetts, The Mathworks (1995).

F. Gouisbaut, D. Peaucelle, A note on stability of time delay systems, IFAC-ROCOND, Toulouse, France, 5-7, July, (2006).

F. Gouisbaut, D. Peaucelle, Delay-dependent stability analysis of linear time delay systems, IFACTDS, L’Aquila, Italy, 10-12 July (2006).

K. Gu, An integral inequality in the stability problem of time - delay systems, Proceedings of the 39th IEEE conference on Decision and Control, Sydney, Australia, 2805-2810, (2000).

H. Gu, Mean square exponential stability in high-order stochastic impulsive BAM neural networks with time-varying delays Neurocomputing 74 (2011) 720-729

S.Haykin, Neural Networks: A Comprehensive Foundation, Prentice-Hall, New-Jersey, 1998.

H. Huang, G. Feng, Delay - dependent stability for uncertain stochastic neural networks with time - varying delay, Physica A 381 (15) (2007) 93 - 103.

Y. Li, L. Zhao, T. Zhang, Global exponential stability and existence of periodic solution of impulsive CohenGrossberg neural networks with distributed delays on time scales Neural Process Lett 33 (2011) 61-81

H. B. Zeng, Y. He, P. Shi, M. Wu, S. P. Xiao, Dissipativity analysis of neural networks with time-varying delays, Neurocomputing 168(2015) 741–746.

C.Y. Lu, H. H. Tsai, T.J. Su, J. S. H. Tsai, C. W. Liao, A Delay - dependent approach to passivity analysis for uncertain neural networks with time - varying delay, Neural Process Lett. 27 (2008) 237 - 246.

E. Yucel, An analysis of global robust stability of delayed dynamical neural networks Neurocomputing 165(2015) 436–443.

Q. Ma, S. Xu , Y. Zou, J. Lu, Stability of stochastic Markovian jump neural networks with mode-dependent delays Neurocomputing 74 (2011) 2157-2163.

J. H. Park, Further results on passivity analysis of delayed cellular neural networks with time - varying delays, Chaos Solitons Fractals 70 (2007) 1546 - 1551.

R. Sathy, P. Balasubramaniam, Stability analysis of fuzzy Markovian jumping Cohen-Grossberg BAM neural networks with mixed time-varying delays Commun Nonlinear Sci Numer Simulat 16 (2011) 2054-2064.

M. Syed Ali, Stability analysis of Markovian Jumping stochastic Cohen–Grossberg neural networks with discrete and distributed time varying delays, Chinese Physics B 6 (2014).

M. Syed Ali, Robust stability of stochastic uncertain recurrent neural networks with Markovian jumping parameters and time-varying delays, Int. J. Mach. Learn. Cyber., 5 (2014) 13–22.

J. Tian, Y. Li, J. Zhao, S. Zhong, Delay-dependent stochastic stability criteria for Markovian jumping neural networks with mode-dependent time-varying delays and partially known transition rates Appl. Math. Comput. 218 (2012) 5769-5781

Z. Wang, H. Shu, J. Fang, X. Liu, Robust stability for stochastic Hopfield neurarl networks with time delays, Nonlinear Anal. Real World. Appl. 7 (2006) 1119 - 1128.

S. Senan, Robustness analysis of uncertain dynamical neural networks with multiple time delays Neural Networks 70 (2015) 53–60.

Z. Wang, S. Lauria, J. Fang, X. Liu, Exponential stability of uncertain stochastic neural networks with mixed time delays, Chaos Solitons Fractals, 32 (2007) 62-72.

L. Xie, Stochastic robust analysis for Markovian jumping neural networks with time delays, ICNC 1 (2005) 386–389.

S. Xu, W. X. Zheng, Passivity analysis of neural networks with time - varying delays, IEEE Trans. Circuit Syst II 56 (4) (2009) 325 - 329.

H. Yang, T. Chu, C. Zhang, Exponential stability of neural networks with variable delays via LMI approach, Chaos Solitons Fractals 30 (2006) 133 - 139.

W. Yu, L. Yao, Global robust stability of neural networks with time varying delays, Journal of Comput. Appl. Math., 206 (2007) 679-687.

J. Yu, G. Sun, Robust stabilization of stochastic Markovian jumping dynamical networks with mixed delays Neurocomputing 86 (2012) 107-115

L. Liu, Q. Zhu, Almost sure exponential stability of numerical solutions to stochastic delay Hopfield neural networks, Appl. Math. Comput. 266(2015) 698 - 712.

W. Xie, Q. Zhu, Mean square exponential stability of stochastic fuzzy delayed Cohen–Grossberg neural networks with expectations in the coefficients, Neurocomputing 166 (2015) 133 - 139.

H. Zhang, M. Dong, Y. C. Wang, N. Sun, Stochastic stability analysis of neutral-type impulsive neural networks with mixed time-varying delays and Markovian jumping, Neurocomputing 73 (2010) 2689-2695

S. Zhu, Y. Shen, L. Liu, Exponential stability of uncertain stochastic neural networks with Markovian switching Neural Process Lett 32 (2010) 293-309

J. Zhu, Q. Zhang, Z. Yuan, Delay-dependent passivity criterion for discrete-time delayed standard neural network model Neurocomputing 73 (2010) 1384-1393.




DOI: https://doi.org/10.37628/ijra.v1i1.152

Refbacks

  • There are currently no refbacks.