带有离散分布式延迟神经网络的不等时滞分割稳定性分析方法

数学物理学报 ›› 2017, Vol. 37 ›› Issue (2): 374-389.

带有离散分布式延迟神经网络的不等时滞分割稳定性分析方法

殷春, 周士伟, 吴姗姗, 程玉华, 魏修岭, 王伟

电子科技大学自动化工程学院成都 611731

收稿日期:2016-07-02 修回日期:2016-12-02 出版日期:2017-04-26 发布日期:2017-04-26
作者简介:殷春,yinchun.86416@163.com
基金资助:
国家自然科学基金（61503064，51502338）和四川省国际合作基金（2015HH0039）

New Unequal Delay Partitioning Methods to Stability Analysis for Neural Networks with Discrete and Distributed Delays

Yin Chun, Zhou Shiwei, Wu Shanshan, Cheng Yuhua, Wei Xiuling, Wang Wei

College of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 611731

Received:2016-07-02 Revised:2016-12-02 Online:2017-04-26 Published:2017-04-26
Supported by:
Supported by the NSFC (61503064, 51502338) and the International Cooperation Project of Sichuan Province (2015HH0039)

摘要/Abstract

摘要： 该文解决了带有离散分布式延迟的神经网络的稳定性分析问题，提出了一种不同于以前方法的新不等时滞分割方法.通过将延迟区间不等地分成多个递减子区间，从而建立一个新颖的包含三次积分项的Lyapunov-Krasovskii函数.其与一些有效的数学技术和新不等时滞分割方法综合在一起，使得新的稳定性标准已被提议减少其保守性.数值仿真实例证明了该文所提出方法的有效性.

关键词: 神经网络, 不等时滞分割, 离散延迟分布, LMI划分

Abstract: This paper deal with the problems of stability analysis for neural networks with with discrete and distributed delays. It addresses the newly unequal delay-partitioning methods which is different from previous methods. By unequally separating the delay interval into multiple diminishing subintervals, a novel Lyapunov-Krasovskii functionals is established including triple integrals terms. And together with some effective mathematical techniques and newly unequal delay-partitioning methods, the new stability criterion has been proposed to reduce the conservatism. Some numerical simulations are given to demonstrate the effectiveness of the proposed techniques comparing with some existing results.

Key words: Neural networks, Unequal delay-partitioning, Discrete and distributed delays, LMI approach

中图分类号:

殷春, 周士伟, 吴姗姗, 程玉华, 魏修岭, 王伟. 带有离散分布式延迟神经网络的不等时滞分割稳定性分析方法[J]. 数学物理学报, 2017, 37(2): 374-389.

Yin Chun, Zhou Shiwei, Wu Shanshan, Cheng Yuhua, Wei Xiuling, Wang Wei. New Unequal Delay Partitioning Methods to Stability Analysis for Neural Networks with Discrete and Distributed Delays[J]. Acta mathematica scientia,Series A, 2017, 37(2): 374-389.

参考文献

[1] Chen F W,Garnier H,Gilson M.Robust identification of continuous-time models with arbitrary time-delay from irregularly sampled data.Journal of Process Control,2015,25:19-27
[2] Zhao Z L,Liu F Z,Xie X C,Liu X H,Tang Z M.Asymptotic stability of bidirectional associative memory neural networks with time-varying delays via delta operator approach.Neurocomputing,2013,117:40-46
[3] Ratnavelu K,Manikandan M,Balasubramaniam P.Synchronization of fuzzy bidirectional associative memory neural networks with various time delays.Applied Mathematics and Computation,2015,270:582-605
[4] Yin C,Chen Y Q,Stark B,Zhong S,Lau E.Fractional-order adaptive minimum energy cognitive lighting control strategy for the hybrid lighting system.Energy and Buildings,2015,87:176-184
[5] Yin C,Chen Y Q,Zhong S M.Fractional-order sliding mode based extremum seeking control of a class of nonlinear system.Automatica,2014,50:3173-3181
[6] He Y,Liu G,Rees D.New delay-dependent stability criteria for neural networks with time-varying delay.IEEE Trans:Neural Networks,2007,18:310-314
[7] He Y,Liu G,Rees D,Wu M.Stability analysis for neural networks with time-varying interval delay.IEEE Trans:Neural Networks,2007,18:1850-1854
[8] Li T,Ye X L.Improved stability criteria of neural networks with time-varying delays:an augmented LKF approach.Neurocomputing,2010,73:1038-1047
[9] Gu K Q.A further refinement of discretized Lyapunov functional method for the stability of time-delay systems.Int J Control,2001,74:967-976
[10] Li Y Y,Zhong S M,Cheng J,Shi K B,Ren J J.New passivity criteria for uncertain neural networks with time-varying delay.Neurocomputing,2016,171(1):1003-1012
[11] Shi K B,Zhong S M,Zhu H,Liu X Z,Zeng Y.New stability analysis for neutral type neural networks with discrete and distributed delays using a multiple integral approach.Journal of the Franklin Instutute,2015,352:155-176
[12] Kharitonov Vladimir L.Predictor based stabilization of neutral type systems with input delay.Automatica,2015,52:125-134
[13] Xiao S,Zhang X.New globally asymptotic stability criteria for delayed cellular neural networks.IEEE Trans:Circuits Systems Ⅱ,2009,56:659-663
[14] Balasubramaniam P,Lakshmanan S,Manivannan A.Rubust stability analysis for Markovian jumping interval neural networks with discrete and distributed time-varing delays.Chaos:Solotons and Fractals,2012,45:483-495
[15] Li T,Song A G,Xue M X,Zhang H T.Stability analysis on delayed neural networks based on an improved delay-partitioning approach.Journal of Computational and Applied Mathematics,2011,235:3086-3095
[16] Zhang H,Liu Z,Huang G,Wang Z.Novel weighting-delaybased stability criteria for recurrent neural networks with time-varying delay.IEEE Trans:Neural Networks,2010,21:91-106
[17] Zhang X,Han Q.New Lyapunov-Krasovskii functionals for global asymptotic stability of delayed neural networks.IEEE Trans:Neural Networks,2009,20:533-539
[18] Tian J K,Xiong W J,Xu F.Improved delay-partitioning method to stability analysis for neural networks with discrete and distributed time-varying delays.Applied Mathematical and Computation,2014,233:152-164
[19] Zeng H,He Y,Wu M,Zhang C.Complete delay-decomposing approach to asymptotic stability for neural networks with time-varying delays.IEEE Trans:Neural Networks,2011,22:806-812
[20] Ge C,Hua C,Guan X.New delay-dependent stability criteria for neural networks with time-varying delay using delay-decomposition approach.IEEE Trans:Neural Networks,2014,25(7):1378-1383
[21] Li C,Liao X.Passivity analysis of neural network with time delay.IEEE Trans,Circuits Systems Ⅱ:Express Briefs,2015,52:471-475
[22] Park P,Ko J W,Jeong C K.Reciprocally convex approach to stability of systems with time-varying delays.Automatica,2011,47:235-238
[23] Shi K B,Zhu H,Zhong S M,Zeng Y,Zhang Y P.Improved delay-dependent stability criteria for neural networks with discrete and distributed time-varying delays using a delay-partitioning approach.Nonlinear Dynamics,2015,79(1):575-592
[24] Hui J J,Kong X Y,Zhang H X,Zhou X.Delay-partitioning approach for system with interval time-varying delay and nonlinear perturbations.Journal of Computation and Applied Mathematics,2015,281:74-81
[25] Xia J W,Park Ju H,Zeng H B.Improved delay-dependent robust stability analysis for neutral-type uncertain neural networks with Markovian jumping parameters and time-varying delays.Neurocomping,2015,149:1198-1205