Robust Exponential Stability of Periodic Solutions for Static Recurrent Neural Networks with Delays

Guang-Hua Zhang; Hong Zhang; Jiangfeng Li; Shanzai Lee

doi:doi:10.11648/j.mlr.20170204.11

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Robust Exponential Stability of Periodic Solutions for Static Recurrent Neural Networks with Delays

Guang-Hua Zhang, Hong Zhang, Jiangfeng Li, Shanzai Lee

Published in Machine Learning Research (Volume 2, Issue 4)

Received: 6 February 2017 Accepted: 22 May 2017 Published: 14 July 2017

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Abstract

In this paper, we study the existence of periodic solutions of time-invariant static recurrent neural networks by using the fixed point theory, Poineare map and Lyapunov function combined with inequality techniques. The static recurrent neural network is a kind of neural network which studies the external states of neurons as variables. And its global robust exponential stability. This paper introduces the research status of artificial neural network, summarizes the research background and development of static recurrent neural network dynamic system, and introduces the main work of this paper. Using the fixed point theory, M. The existence of periodic solutions and the global robust exponential stability of the static recursive neural network with variable delays and the existence of almost periodic solutions of the static recursive neural network of the partitioned time are studied by combining the properties of the matrix and the Lyapunov function combined with the inequality technique. Global exponential stability, the stability conditions of the corresponding problem are obtained respectively, and the results of the related research are generalized. Using Lyapunov. The stability of the quasi - static neural recursive neural network and the stability of the periodic solution are studied. The condition of the stationary static recursive neural network is obtained and the correctness of the condition is illustrated. Considering the influence of stochastic perturbation on the dynamic behavior of static recurrent neural network, the static recursive neural network with time delay and the static recursive neural network with distributed time delay are studied by using the infinitesimal operator, Ito formula and the convergence theorem of martingales. Global critical exponential stability of quasi - static neural network with stochastic perturbation. The static recursive neural network with Markovian modulation and the time-delay static recurrent neural network model considering both random perturbation and Markovian switching are studied. The linear matrix inequality, the finite state space Markov chain property and the Lyapunov-krasovskii function, The judgment condition of the global exponential stability of the system is obtained. Firstly, the global exponential stability problem of quasi - static neural neural network with time - delay and recursive neural network is studied by using the generalized Halanay inequality. Then the stability of the Markovian response sporadic static recurrent neural network is studied by combining the properties of Markov chain.

Published in	Machine Learning Research (Volume 2, Issue 4)
DOI	10.11648/j.mlr.20170204.11
Page(s)	113-118
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Robust Exponential Stability, Static Recurrent Neural Networks

References

[1]	Linshan Wang and Daoyi Xu. Global exponential stability of Hopfeild reaction-diffusion neural networks with time-varying delays. Science in China (Series F), 2003, 46 (6): 466-474.
[2]	Linshan. Wang, Yiying. Gao. Global exponential robust stability of reaction-diffusion interval neural networks with time-varying delays. Phys. Lett. A, 2006, 350: 342-348.
[3]	Linshan Wang and Daoyi Xu. Asymptotic behavior ofa class of reaction-diffusion equations with delays. Journal Mathematical Analysis and Applications, 2003, 28 1 (2): 439-453 (SCI1DS: 691EF).
[4]	Linshan Wang, Yangfan Wang. Stochastic exponential stability of the delayed. reaction-diffusion recurrent neural networks with Markovian jumping parameters. Physics Letters A, 2007, 356 (4), 346-352
[5]	Linshan Wang, Yan Zhang, Zhe Zhang, Yangfan Wang. LMI-based approach for global exponential robust stability for rection-diffusion uncertain neural networks with time-varying delay. Chaos, Solitons and Fracals 41 (2009) 900-905.
[6]	Linshan Wang, Ruojun Zhang, Global exponential stability of reaction-diffusion cellular neural networks with S-type distributed time delays, Nonlinear Analysis: Real World Applications, 2009, 10 (2): l101-1l13.
[7]	P. Balasubramaniam, R. Rakkiyappan. Global asymptotic stability of stochastic recurrent neural networks with multiple discrete delays and unbounded distributed delays. Applied Mathematics and Computation, 2008, 204 (2): 680-686.
[8]	Yah Lv, Wei Lv, Jianhua Sun. Convergence dynamics of stochastic reaction-diffusion recurrent neural networks with continuously distributed delays. Nonlinear Analysis: Real World Applications, 2008, 9 (4): 1590-1606.
[9]	Zidong Wang, Huisheng Shu, Jian’an Fang, Xiaohui Liu. Robust stability for stochastic Hopfield neural networks with time delays. Nonlinear Analysis: Real World Applications, 2006, 7 (5): 1119-1 128.
[10]	Yonghui Sun, Jinde Cao. pth moment exponential stability of stochastic recurrent neural networks with time-varying delays. Nonlinear Analysis: Real World Applications, 2007, 8 (4): 1171-1185.

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APA Style

Guang-Hua Zhang, Hong Zhang, Jiangfeng Li, Shanzai Lee. (2017). Robust Exponential Stability of Periodic Solutions for Static Recurrent Neural Networks with Delays. Machine Learning Research, 2(4), 113-118. https://doi.org/10.11648/j.mlr.20170204.11

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ACS Style

Guang-Hua Zhang; Hong Zhang; Jiangfeng Li; Shanzai Lee. Robust Exponential Stability of Periodic Solutions for Static Recurrent Neural Networks with Delays. Mach. Learn. Res. 2017, 2(4), 113-118. doi: 10.11648/j.mlr.20170204.11

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AMA Style

Guang-Hua Zhang, Hong Zhang, Jiangfeng Li, Shanzai Lee. Robust Exponential Stability of Periodic Solutions for Static Recurrent Neural Networks with Delays. Mach Learn Res. 2017;2(4):113-118. doi: 10.11648/j.mlr.20170204.11

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@article{10.11648/j.mlr.20170204.11,
  author = {Guang-Hua Zhang and Hong Zhang and Jiangfeng Li and Shanzai Lee},
  title = {Robust Exponential Stability of Periodic Solutions for Static Recurrent Neural Networks with Delays},
  journal = {Machine Learning Research},
  volume = {2},
  number = {4},
  pages = {113-118},
  doi = {10.11648/j.mlr.20170204.11},
  url = {https://doi.org/10.11648/j.mlr.20170204.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mlr.20170204.11},
  abstract = {In this paper, we study the existence of periodic solutions of time-invariant static recurrent neural networks by using the fixed point theory, Poineare map and Lyapunov function combined with inequality techniques. The static recurrent neural network is a kind of neural network which studies the external states of neurons as variables. And its global robust exponential stability. This paper introduces the research status of artificial neural network, summarizes the research background and development of static recurrent neural network dynamic system, and introduces the main work of this paper. Using the fixed point theory, M. The existence of periodic solutions and the global robust exponential stability of the static recursive neural network with variable delays and the existence of almost periodic solutions of the static recursive neural network of the partitioned time are studied by combining the properties of the matrix and the Lyapunov function combined with the inequality technique. Global exponential stability, the stability conditions of the corresponding problem are obtained respectively, and the results of the related research are generalized. Using Lyapunov. The stability of the quasi - static neural recursive neural network and the stability of the periodic solution are studied. The condition of the stationary static recursive neural network is obtained and the correctness of the condition is illustrated. Considering the influence of stochastic perturbation on the dynamic behavior of static recurrent neural network, the static recursive neural network with time delay and the static recursive neural network with distributed time delay are studied by using the infinitesimal operator, Ito formula and the convergence theorem of martingales. Global critical exponential stability of quasi - static neural network with stochastic perturbation. The static recursive neural network with Markovian modulation and the time-delay static recurrent neural network model considering both random perturbation and Markovian switching are studied. The linear matrix inequality, the finite state space Markov chain property and the Lyapunov-krasovskii function, The judgment condition of the global exponential stability of the system is obtained. Firstly, the global exponential stability problem of quasi - static neural neural network with time - delay and recursive neural network is studied by using the generalized Halanay inequality. Then the stability of the Markovian response sporadic static recurrent neural network is studied by combining the properties of Markov chain.},
 year = {2017}
}

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TY  - JOUR
T1  - Robust Exponential Stability of Periodic Solutions for Static Recurrent Neural Networks with Delays
AU  - Guang-Hua Zhang
AU  - Hong Zhang
AU  - Jiangfeng Li
AU  - Shanzai Lee
Y1  - 2017/07/14
PY  - 2017
N1  - https://doi.org/10.11648/j.mlr.20170204.11
DO  - 10.11648/j.mlr.20170204.11
T2  - Machine Learning Research
JF  - Machine Learning Research
JO  - Machine Learning Research
SP  - 113
EP  - 118
PB  - Science Publishing Group
SN  - 2637-5680
UR  - https://doi.org/10.11648/j.mlr.20170204.11
AB  - In this paper, we study the existence of periodic solutions of time-invariant static recurrent neural networks by using the fixed point theory, Poineare map and Lyapunov function combined with inequality techniques. The static recurrent neural network is a kind of neural network which studies the external states of neurons as variables. And its global robust exponential stability. This paper introduces the research status of artificial neural network, summarizes the research background and development of static recurrent neural network dynamic system, and introduces the main work of this paper. Using the fixed point theory, M. The existence of periodic solutions and the global robust exponential stability of the static recursive neural network with variable delays and the existence of almost periodic solutions of the static recursive neural network of the partitioned time are studied by combining the properties of the matrix and the Lyapunov function combined with the inequality technique. Global exponential stability, the stability conditions of the corresponding problem are obtained respectively, and the results of the related research are generalized. Using Lyapunov. The stability of the quasi - static neural recursive neural network and the stability of the periodic solution are studied. The condition of the stationary static recursive neural network is obtained and the correctness of the condition is illustrated. Considering the influence of stochastic perturbation on the dynamic behavior of static recurrent neural network, the static recursive neural network with time delay and the static recursive neural network with distributed time delay are studied by using the infinitesimal operator, Ito formula and the convergence theorem of martingales. Global critical exponential stability of quasi - static neural network with stochastic perturbation. The static recursive neural network with Markovian modulation and the time-delay static recurrent neural network model considering both random perturbation and Markovian switching are studied. The linear matrix inequality, the finite state space Markov chain property and the Lyapunov-krasovskii function, The judgment condition of the global exponential stability of the system is obtained. Firstly, the global exponential stability problem of quasi - static neural neural network with time - delay and recursive neural network is studied by using the generalized Halanay inequality. Then the stability of the Markovian response sporadic static recurrent neural network is studied by combining the properties of Markov chain.
VL  - 2
IS  - 4
ER  -

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Author Information

Guang-Hua Zhang

College of Computer Science, Chongqing University, Chongqing, China
Hong Zhang

School of Information, Beijing Wuzi University, Beijing, China
Jiangfeng Li

School of Science, Jiujiang University, Jiujiang, China
Shanzai Lee

School of Information, Beijing Wuzi University, Beijing, China

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Plain Text BibTeX RIS

APA Style

Guang-Hua Zhang, Hong Zhang, Jiangfeng Li, Shanzai Lee. (2017). Robust Exponential Stability of Periodic Solutions for Static Recurrent Neural Networks with Delays. Machine Learning Research, 2(4), 113-118. https://doi.org/10.11648/j.mlr.20170204.11

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ACS Style

Guang-Hua Zhang; Hong Zhang; Jiangfeng Li; Shanzai Lee. Robust Exponential Stability of Periodic Solutions for Static Recurrent Neural Networks with Delays. Mach. Learn. Res. 2017, 2(4), 113-118. doi: 10.11648/j.mlr.20170204.11

Copy | Download

AMA Style

Guang-Hua Zhang, Hong Zhang, Jiangfeng Li, Shanzai Lee. Robust Exponential Stability of Periodic Solutions for Static Recurrent Neural Networks with Delays. Mach Learn Res. 2017;2(4):113-118. doi: 10.11648/j.mlr.20170204.11

Copy | Download

@article{10.11648/j.mlr.20170204.11,
  author = {Guang-Hua Zhang and Hong Zhang and Jiangfeng Li and Shanzai Lee},
  title = {Robust Exponential Stability of Periodic Solutions for Static Recurrent Neural Networks with Delays},
  journal = {Machine Learning Research},
  volume = {2},
  number = {4},
  pages = {113-118},
  doi = {10.11648/j.mlr.20170204.11},
  url = {https://doi.org/10.11648/j.mlr.20170204.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mlr.20170204.11},
  abstract = {In this paper, we study the existence of periodic solutions of time-invariant static recurrent neural networks by using the fixed point theory, Poineare map and Lyapunov function combined with inequality techniques. The static recurrent neural network is a kind of neural network which studies the external states of neurons as variables. And its global robust exponential stability. This paper introduces the research status of artificial neural network, summarizes the research background and development of static recurrent neural network dynamic system, and introduces the main work of this paper. Using the fixed point theory, M. The existence of periodic solutions and the global robust exponential stability of the static recursive neural network with variable delays and the existence of almost periodic solutions of the static recursive neural network of the partitioned time are studied by combining the properties of the matrix and the Lyapunov function combined with the inequality technique. Global exponential stability, the stability conditions of the corresponding problem are obtained respectively, and the results of the related research are generalized. Using Lyapunov. The stability of the quasi - static neural recursive neural network and the stability of the periodic solution are studied. The condition of the stationary static recursive neural network is obtained and the correctness of the condition is illustrated. Considering the influence of stochastic perturbation on the dynamic behavior of static recurrent neural network, the static recursive neural network with time delay and the static recursive neural network with distributed time delay are studied by using the infinitesimal operator, Ito formula and the convergence theorem of martingales. Global critical exponential stability of quasi - static neural network with stochastic perturbation. The static recursive neural network with Markovian modulation and the time-delay static recurrent neural network model considering both random perturbation and Markovian switching are studied. The linear matrix inequality, the finite state space Markov chain property and the Lyapunov-krasovskii function, The judgment condition of the global exponential stability of the system is obtained. Firstly, the global exponential stability problem of quasi - static neural neural network with time - delay and recursive neural network is studied by using the generalized Halanay inequality. Then the stability of the Markovian response sporadic static recurrent neural network is studied by combining the properties of Markov chain.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Robust Exponential Stability of Periodic Solutions for Static Recurrent Neural Networks with Delays
AU  - Guang-Hua Zhang
AU  - Hong Zhang
AU  - Jiangfeng Li
AU  - Shanzai Lee
Y1  - 2017/07/14
PY  - 2017
N1  - https://doi.org/10.11648/j.mlr.20170204.11
DO  - 10.11648/j.mlr.20170204.11
T2  - Machine Learning Research
JF  - Machine Learning Research
JO  - Machine Learning Research
SP  - 113
EP  - 118
PB  - Science Publishing Group
SN  - 2637-5680
UR  - https://doi.org/10.11648/j.mlr.20170204.11
AB  - In this paper, we study the existence of periodic solutions of time-invariant static recurrent neural networks by using the fixed point theory, Poineare map and Lyapunov function combined with inequality techniques. The static recurrent neural network is a kind of neural network which studies the external states of neurons as variables. And its global robust exponential stability. This paper introduces the research status of artificial neural network, summarizes the research background and development of static recurrent neural network dynamic system, and introduces the main work of this paper. Using the fixed point theory, M. The existence of periodic solutions and the global robust exponential stability of the static recursive neural network with variable delays and the existence of almost periodic solutions of the static recursive neural network of the partitioned time are studied by combining the properties of the matrix and the Lyapunov function combined with the inequality technique. Global exponential stability, the stability conditions of the corresponding problem are obtained respectively, and the results of the related research are generalized. Using Lyapunov. The stability of the quasi - static neural recursive neural network and the stability of the periodic solution are studied. The condition of the stationary static recursive neural network is obtained and the correctness of the condition is illustrated. Considering the influence of stochastic perturbation on the dynamic behavior of static recurrent neural network, the static recursive neural network with time delay and the static recursive neural network with distributed time delay are studied by using the infinitesimal operator, Ito formula and the convergence theorem of martingales. Global critical exponential stability of quasi - static neural network with stochastic perturbation. The static recursive neural network with Markovian modulation and the time-delay static recurrent neural network model considering both random perturbation and Markovian switching are studied. The linear matrix inequality, the finite state space Markov chain property and the Lyapunov-krasovskii function, The judgment condition of the global exponential stability of the system is obtained. Firstly, the global exponential stability problem of quasi - static neural neural network with time - delay and recursive neural network is studied by using the generalized Halanay inequality. Then the stability of the Markovian response sporadic static recurrent neural network is studied by combining the properties of Markov chain.
VL  - 2
IS  - 4
ER  -

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