Linear matrix inequality approach for robust stability analysis for stochastic neural networks with time-varying delay

doi:10.1088/1674-1056/20/4/040204

中国物理B ›› 2011, Vol. 20 ›› Issue (4): 40204-040204.doi: 10.1088/1674-1056/20/4/040204

Linear matrix inequality approach for robust stability analysis for stochastic neural networks with time-varying delay

S. Lakshmanan, P. Balasubramaniam

Department of Mathematics, Gandhigram Rural University, Gandhigram { 624 302, Tamilnadu, India

收稿日期:2010-10-29 修回日期:2010-11-29 出版日期:2011-04-15 发布日期:2011-04-15
基金资助:
Project supported by the Science Foundation of the Department of Science and Technology, New Delhi, India (Grant No. SR/S4/MS:485/07).

Linear matrix inequality approach for robust stability analysis for stochastic neural networks with time-varying delay

S. Lakshmanan and P. Balasubramaniam^†

Department of Mathematics, Gandhigram Rural University, Gandhigram -624 302, Tamilnadu, India

Received:2010-10-29 Revised:2010-11-29 Online:2011-04-15 Published:2011-04-15
Supported by:
Project supported by the Science Foundation of the Department of Science and Technology, New Delhi, India (Grant No. SR/S4/MS:485/07).

摘要/Abstract

摘要： This paper studies the problem of linear matrix inequality (LMI) approach to robust stability analysis for stochastic neural networks with a time-varying delay. By developing a delay decomposition approach, the information of the delayed plant states can be taken into full consideration. Based on the new Lyapunov-Krasovskii functional, some inequality techniques and stochastic stability theory, new delay-dependent stability criteria are obtained in terms of LMIs. The proposed results prove the less conservatism, which are realized by choosing new Lyapunov matrices in the decomposed integral intervals. Finally, numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed LMI method.

Abstract: This paper studies the problem of linear matrix inequality (LMI) approach to robust stability analysis for stochastic neural networks with a time-varying delay. By developing a delay decomposition approach, the information of the delayed plant states can be taken into full consideration. Based on the new Lyapunov-Krasovskii functional, some inequality techniques and stochastic stability theory, new delay-dependent stability criteria are obtained in terms of LMIs. The proposed results prove the less conservatism, which are realized by choosing new Lyapunov matrices in the decomposed integral intervals. Finally, numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed LMI method.

Key words: delay-dependent stability, linear matrix inequality, Lyapunov--Krasovskii functional, stochastic neural networks

中图分类号: (Stochastic processes)

02.50.Ey

02.50.Fz (Stochastic analysis) 07.05.Mh (Neural networks, fuzzy logic, artificial intelligence)

S. Lakshmanan, P. Balasubramaniam. Linear matrix inequality approach for robust stability analysis for stochastic neural networks with time-varying delay[J]. 中国物理B, 2011, 20(4): 40204-040204.

S. Lakshmanan and P. Balasubramaniam. Linear matrix inequality approach for robust stability analysis for stochastic neural networks with time-varying delay[J]. Chin. Phys. B, 2011, 20(4): 40204-040204.

参考文献 31

[1]	Haykin S 1998 Neural Networks: A Comprehensive Foundation (New Jersey: Prentice Hall)
[2]	Chen T and Rong L 2003 Phys. Lett. A 317 436
[3]	Chen Y and Wu Y 2009 Neurocomputing 72 1065
[4]	Chen J, Sun J, Liu G P and Rees D 2010 Phys. Lett. A doi: 10.1016/j.physleta.2010.08.070.
[5]	Qiu F, Cui B and Wu W 2009 Appl. Math. Modelling 33 198
[6]	Fu X and Li X 2011 Commun. Nonlinear Sci. Numer. Simul. 16 435.
[7]	Li D, Wang H, Yang D, Zhang X H and Wang S L 2008 Chin. Phys. B 17 4091
[8]	Li X and Chen Z 2009 Nonlinear Anal.: Real World Appl. 10 3253
[9]	Shao J L, Huang T Z and Zhou S 2009 Neurocomputing 72 1993
[10]	Chen W Y 2002 Int. J. Systems Sci. 33 917
[11]	Feng W, Yang S X, Fu W and Wu H 2009 Chaos, Solitons and Fractals 41 414
[12]	Chen W H and Lu X 2008 Phys. Lett. A 372 1061
[13]	Wang Z, Lauria S, Fang J and Liu X 2007 Chaos, Solitons and Fractals 32 62 %Lett. A} 351 153.
[14]	Huang H and Feng G 2007 Physica A 381 93
[15]	Wang Z, Shu H, Fang J and Liu X 2006 Nonlinear Anal.: Real World Appl. 7 1119
[16]	Zhang J, Shi P and Qiu J 2007 Nonlinear Anal.: Real World Appl. 8 1349
[17]	Yu J, Zhang K and Fei S 2009 Commun. Nonlinear Sci. Numer. Simul. 14 1582
[18]	Li H, Chen B, Zhou Q and Fang S 2008 Phys. Lett. A 372 3385
[19]	Wu Y, Wu Y and Chen Y 2009 Neurocomputing 72 2379
[20]	Rakkiyappan R, Balasubramaniam P and Lakshmanan S 2008 Phys. Lett. A 37 5290
[21]	Huang C, He Y and Wang H 2008 Comput. Math. Appl. 56 1773
[22]	Tang Z H and Fang J A 2008 Chin. Phys. B 17 4080
[23]	Chen D L and Zhang W D 2008 Chin. Phys. B 17 1506
[24]	Zhang B and Xu S, Zong G and Zou Y 2009 IEEE Trans. Circuits Syst. I 56 1241
[25]	Zhang H G, Fu J, Ma T D and Tong S C 2009 Chin. Phys. B 18 3325
[26]	Feng W, Yang S X and Wu H 2009 Chaos, Solitons and Fractals 42 2095
[27]	Wu H, Liao X, Guo S, Feng W and Wang Z 2009 Neurocomputing 72 3263
[28]	Kwon O M, Lee S M and Park J H 2010 Phys. Lett. A 374 1232
[29]	Zhu X L and Yang G H 2010 Int. J. Robust Nonlinear Control 20 596
[30]	Yue D, Tian E, Zhang Y and Peng C 2009 Int. J. Robust Nonlinear Control 19 377
[31]	Gu K 2000 Proceedings of 39th IEEE Conference on Decision and Control p. 2805 endfootnotesize

Linear matrix inequality approach for robust stability analysis for stochastic neural networks with time-varying delay

Linear matrix inequality approach for robust stability analysis for stochastic neural networks with time-varying delay

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 31

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Kheder Suleiman, Xuelan Zhang(张雪岚), Erhui Wang(王二辉),Shengna Liu(刘圣娜), and Liancun Zheng(郑连存). Anomalous diffusion in branched elliptical structure[J]. 中国物理B, 2023, 32(1): 10202-010202.
[2]	Kheder Suleiman, Xue-Lan Zhang(张雪岚), Sheng-Na Liu(刘圣娜), and Lian-Cun Zheng(郑连存). Diffusion dynamics in branched spherical structure[J]. 中国物理B, 2022, 31(11): 110202-110202.
[3]	Liang'an Huo(霍良安) and Xiaomin Chen(陈晓敏). Dynamical behavior and optimal impulse control analysis of a stochastic rumor spreading model[J]. 中国物理B, 2022, 31(11): 110204-110204.
[4]	Yuhuai Zhang(张宇槐) and Jianjun Zhu(朱建军). Ergodic stationary distribution of a stochastic rumor propagation model with general incidence function[J]. 中国物理B, 2022, 31(6): 60202-060202.
[5]	Liang'an Huo(霍良安) and Yafang Dong(董雅芳). Dynamics and near-optimal control in a stochastic rumor propagation model incorporating media coverage and Lévy noise[J]. 中国物理B, 2022, 31(3): 30202-030202.
[6]	Anwarud Din and Yongjin Li(黎永锦). Stochastic optimal control for norovirus transmission dynamics by contaminated food and water[J]. 中国物理B, 2022, 31(2): 20202-020202.
[7]	Liang'an Huo(霍良安) and Xiaomin Chen(陈晓敏). Near-optimal control of a stochastic rumor spreading model with Holling II functional response function and imprecise parameters[J]. 中国物理B, 2021, 30(12): 120205-120205.
[8]	Liang-An Huo(霍良安), Ya-Fang Dong(董雅芳), and Ting-Ting Lin(林婷婷). Dynamics of a stochastic rumor propagation model incorporating media coverage and driven by Lévy noise[J]. 中国物理B, 2021, 30(8): 80201-080201.
[9]	苏桂锋, 李晓温, 张小兵, 张一. Finite density scaling laws of condensation phase transition in zero-range processes on scale-free networks[J]. 中国物理B, 2020, 29(8): 88904-088904.
[10]	张金鹏, 张玉石, 许心瑜, 李清亮, 吴家骥. Estimation of sea clutter inherent Doppler spectrum from shipborne S-band radar sea echo[J]. 中国物理B, 2020, 29(6): 68402-068402.
[11]	田波, 夏萍, 刘莉, 吴蒙然, 郭树勇. Existence of spontaneous symmetry breaking in two-lane totally asymmetric simple exclusion processes with an intersection[J]. 中国物理B, 2020, 29(5): 50505-050505.
[12]	Hossam A. Ghany, Abd-Allah Hyder, M Zakarya. Exact solutions of stochastic fractional Korteweg de-Vries equation with conformable derivatives[J]. 中国物理B, 2020, 29(3): 30203-030203.
[13]	王杰, 宁丽娟. Current transport and mass separation for an asymmetric fluctuation system with correlated noises[J]. 中国物理B, 2018, 27(1): 10501-010501.
[14]	雷佑铭, 张红霞. Homoclinic and heteroclinic chaos in nonlinear systems driven by trichotomous noise[J]. 中国物理B, 2017, 26(3): 30502-030502.
[15]	田波, 姜锐, 胡茂彬, 贾斌. Spurious symmetry-broken phase in a bidirectional two-lane ASEP with narrow entrances[J]. 中国物理B, 2017, 26(2): 20503-020503.