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

Abstract

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

CLC Number:

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.

Trendmd

References

[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

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

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 10

[1]	Ren Hongyue, Zhou Liqun. Mean Square Exponential Synchronization of a Class of Proportional Delay Stochastic Neural Networks and Its Application [J]. Acta mathematica scientia,Series A, 2025, 45(3): 888-901.
[2]	Wu Zekang, Wang Xiaoli, Han Wenjing, Li Jinhong. Solving the Forward and Inverse Problems of Extended Fifth-Order mKdV Equation Via Physics-Informed Neural Networks [J]. Acta mathematica scientia,Series A, 2024, 44(2): 484-499.
[3]	Xingshou Huang,Ricai Luo,Wusheng Wang. Stability Analysis for a Class Neural Network with Proportional Delay Based on the Gronwall Integral Inequality [J]. Acta mathematica scientia,Series A, 2020, 40(3): 824-832.
[4]	Yao Zou,Chunna Zeng,Jin Hu. Global Exponential Periodicity of Complex-Valued Neural Networks with Discontinuous Activation Functions [J]. Acta mathematica scientia,Series A, 2019, 39(5): 1192-1204.
[5]	Qinghua Zhou,Li Wan,Jie Liu. Global Attracting Set for Neutral Type Hopfield Neural Networks with Time-Varying Delays [J]. Acta mathematica scientia,Series A, 2019, 39(4): 823-831.
[6]	Luo Ricai, Xu Honglei, Wang Wusheng. Globally Asymptotic Stability of A New Class of Neutral Neural Networks with Time-Varying Delays [J]. Acta mathematica scientia,Series A, 2015, 35(3): 634-640.
[7]	ZHANG Ruo-Jun, WANG Lin-Shan. Almost Periodic Solutions for Cellular Neural Networks with Distributed Delays [J]. Acta mathematica scientia,Series A, 2011, 31(2): 422-429.
[8]	YU Guo-Hua. The Geometric Rate of Approximation of Neural Network in L^p-Space [J]. Acta mathematica scientia,Series A, 2010, 30(3): 848-856.
[9]	WANG Hong-Chu, HU Shi-Geng. Exponential Stability for Stochastic Neural Networks with Multiple Delays: an LMI Approach [J]. Acta mathematica scientia,Series A, 2010, 30(1): 42-53.
[10]	Liu Bingwen;Hunang Lihong. Existence and Exponential Stability of Almost Periodic Solutions for Cellular Neural Networks with Delays [J]. Acta mathematica scientia,Series A, 2007, 27(6): 1082-1088.
[11]	Chen Wuhua; Lu Xiaomei; Li Qunhong; Guan Zhihong. Exponential Stability in Mean Square for Stochastic Hopfield Delay Neural Networks: an LMI Approach [J]. Acta mathematica scientia,Series A, 2007, 27(1): 109-117.
[12]	CENG Zhi-Gang, LIAO Xiao-Cuan. Global Stability for Neural Networks with Unbouned Time Varying Delays [J]. Acta mathematica scientia,Series A, 2005, 25(5): 621-626.
[13]	ZHOU Guan-Zhen. On Approximation by Neural and Translation Networks in B_a Spaces [J]. Acta mathematica scientia,Series A, 2005, 25(4): 569-576.
[14]	ZHANG Qiang, MA Run-Nian. Delay dependent Stability of Cellular Neural Networks with Delays [J]. Acta mathematica scientia,Series A, 2004, 4(6): 694-698.
[15]	DIAO Hong-Yong, WANGGuang-Lan. Existence and Global Attractivity of Almost Periodic Solutions for Hopfield Neural \|Networks \|with Variable Delay [J]. Acta mathematica scientia,Series A, 2004, 4(6): 723-729.