State Estimation of Complex-Valued Neural Networks With Leakage Delay and Mixed Additive Time-Varying Delays

LIU Libin; PAN Heping

doi:10.21656/1000-0887.400174

Volume 40 Issue 11

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LIU Libin, PAN Heping. State Estimation of Complex-Valued Neural Networks With Leakage Delay and Mixed Additive Time-Varying Delays[J]. Applied Mathematics and Mechanics, 2019, 40(11): 1246-1258. doi: 10.21656/1000-0887.400174

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State Estimation of Complex-Valued Neural Networks With Leakage Delay and Mixed Additive Time-Varying Delays

doi: 10.21656/1000-0887.400174

LIU Libin¹,
PAN Heping^1,2

¹School of Finance, Chongqing Technology and Business University, Chongqing 400067, P.R.China;²Institute of Advanced Studies and Business School, Chengdu University,Chengdu 610106, P.R.China

Funds: The National Social Science Fund of China(17BGL231)

Received Date: 2019-05-20
Rev Recd Date: 2019-07-28
Publish Date: 2019-11-01

Abstract

Abstract

The state estimation of complex-valued neural networks with leakage delay and both discrete and distributed additive time-varying delays was studied. In the case where the activation function of the network was not required to be separated, through construction of the appropriate Lyapunov-Krasovskii functionals, and with the free weight matrix, the matrix inequality and the reciprocal convex combination method, the state of the neuron was estimated by means of observable output measurements. In addition, complex-valued linear matrix inequalities related to time delays were given to ensure the global asymptotic stability of the error-state model. Finally, numerical simulation examples verify the validity of the theoretical analysis.
- leakage delay,
- additive time-varying delay,
- complex-valued neural network,
- linear matrix inequality,
- state estimation

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References(21)

References

[1]	HIROSE A. Dynamics of fully complex-valued neural networks[J]. Electronics Letters,1992,28(16): 1492-1494.
[2]	LEE D L. Relaxation of the stability condition of the complex-valued neural networks[J]. IEEE Transactions on Neural Networks,2001,12(5): 1260-1262.
[3]	张磊, 宋乾坤. 带有比例时滞的复值神经网络全局指数稳定性[J]. 应用数学和力学, 2018,39(5): 584-591.(ZHANG Lei, SONG Qiankun. Global exponential stability of complex-valued neural networks with proportional delays[J]. Applied Mathematics and Mechanics,2018,39(5): 584-591.(in Chinese))
[4]	NITTA T. An analysis of the fundamental structure of complex-valued neurons[J]. Neural Processing Letters,2000,12(3): 239-246.
[5]	ZHOU W, ZURADA J M. Discrete-time recurrent neural networks with complex-valued linear threshold neurons[J].IEEE Transactions on Circuits and Systems Ⅱ: Express Briefs,2009,56(8): 669-673.
[6]	JANKOWSKI S, LOZOWSKI A, ZURADA J M. Complex-valued multistate neural associative memory[J]. IEEE Transactions on Neural Networks,1996,7(6): 1491-1496.
[7]	LIU X W, CHEN T P. Global exponential stability for complex-valued recurrent neural networks with asynchronous time delays[J]. IEEE Transactions on Neural Networks and Learning Systems,2016,27(3): 593-606.
[8]	曹进德, 林怡平. 一类时滞神经网络模型的稳定性[J]. 应用数学和力学, 1999,20(8): 851-855.(CAO Jinde, LIN Yiping. Stability of a class of neural network models with delay[J]. Applied Mathematics and Mechanics,1999,20(8): 851-855.(in Chinese))
[9]	BAI X Z, WANG Z D, ZOU L, et al. Target tracking for wireless localization systems with degraded measurements and quantization effects[J]. IEEE Transactions on Industrial Electronics,2018,〖STHZ〗 65(12): 9687-9697.
[10]	WANG F, WANG Z D, LIANG J L, et al. Resilient filtering for linear time-varying repetitive processes under uniform quantizations and round-robin protocols[J]. IEEE Transactions on Circutts and Systems Ⅰ: Regular Papers,2018,65(9): 2992-3004.
[11]	CHEN X F, ZHAO Z J, SONG Q K, et al. Multistability of complex-valued neural networks with time-varying delays[J]. Applied Mathematics and Computation,2017,294: 18-35.
[12]	HANG H, WANG X Y, LIN X H. Synchronization of complex-valued neural network with sliding mode control[J]. Journal of the Franklin Institute,2016,353(2): 345-358.
[13]	LIU Y R, WANG Z D, LIU X H. Global asymptotic stability of generalized bi-directional associative memory networks with discrete and distributed delays[J]. Chaos, Solitons and Fractal s, 2006,28(3): 793-803.
[14]	LAM J, GAO H, WANG C. Stability analysis for continuous systems with two additive time-varying delay components[J]. Systems and Control Letters,2007,56(1): 16-24.
[15]	CHEN X F, SONG Q K. State estimation for quaternion-valued neural networks with multiple time delays[J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems,2017. DOI: 10.1109/TSMC.2017.2776940.
[16]	曾德强, 吴开腾, 宋乾坤, 等. 时滞神经网络随机抽样控制的状态估计[J]. 应用数学和力学, 2018,39(7): 821-832.(ZENG Deqiang, WU Kaiteng, SONG Qiankun, et al. State estimation for delayed neural networks with stochastic sampled-data control[J]. Applied Mathematics and Mechanics,2018,39(7): 821-832.(in Chinese))
[17]	HUANG H, FENG G, CAO J D. Robust state estimation for uncertain neural networks with time-varying delay[J].IEEE Transactions on Neural Networks,2008,19(8): 1329-1339.
[18]	WANG H W, SONG Q K. State estimation for neural networks with mixed interval time-varying delays[J]. Neurocomputing,2010,73(7/9): 1281-1288.
[19]	WU Z G, SHI P, SU H Y, et al. State estimation for discrete-time neural networks with time-varying delay[J]. International Journal of Systems Science,2012,43(4): 647-655.
[20]	YAN L, ZHANG S J, DING D R, et al. H_∞ state estimation for memristive neural networks with multiple fading measurements[J]. Neurocomputing,2017,230: 23-29.
[21]	LIANG J, LI K L, SONG Q K, et al. State estimation of complex-valued neural networks with two additive time-varying delays[J]. Neurocomputing,2018,309: 54-61.