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State Estimation for Discrete‐Time Stochastic Neural Networks with Mixed Delays

Author

Listed:
  • Liyuan Hou
  • Hong Zhu
  • Shouming Zhong
  • Yong Zeng
  • Lin Shi

Abstract

This paper investigates the analysis problem for stability of discrete‐time neural networks (NNs) with discrete‐ and distribute‐time delay. Stability theory and a linear matrix inequality (LMI) approach are developed to establish sufficient conditions for the NNs to be globally asymptotically stable and to design a state estimator for the discrete‐time neural networks. Both the discrete delay and distribute delays employ decomposing the delay interval approach, and the Lyapunov‐Krasovskii functionals (LKFs) are constructed on these intervals, such that a new stability criterion is proposed in terms of linear matrix inequalities (LMIs). Numerical examples are given to demonstrate the effectiveness of the proposed method and the applicability of the proposed method.

Suggested Citation

  • Liyuan Hou & Hong Zhu & Shouming Zhong & Yong Zeng & Lin Shi, 2014. "State Estimation for Discrete‐Time Stochastic Neural Networks with Mixed Delays," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:209486
    DOI: 10.1155/2014/209486
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    References listed on IDEAS

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    1. Jun Cheng & Hong Zhu & Shouming Zhong & Yuping Zhang, 2012. "Robust Stability of Switched Delay Systems with Average Dwell Time under Asynchronous Switching," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    2. Zhang, Qiang & Wei, Xiaopeng & Xu, Jin, 2008. "Delay-dependent exponential stability criteria for non-autonomous cellular neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 36(4), pages 985-990.
    3. Jun Cheng & Hong Zhu & Shouming Zhong & Yuping Zhang, 2012. "Robust Stability of Switched Delay Systems with Average Dwell Time under Asynchronous Switching," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-17, October.
    4. Wang, Zidong & Shu, Huisheng & Liu, Yurong & Ho, Daniel W.C. & Liu, Xiaohui, 2006. "Robust stability analysis of generalized neural networks with discrete and distributed time delays," Chaos, Solitons & Fractals, Elsevier, vol. 30(4), pages 886-896.
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