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Global μ‐Stability of Impulsive Complex‐Valued Neural Networks with Leakage Delay and Mixed Delays

Author

Listed:
  • Xiaofeng Chen
  • Qiankun Song
  • Yurong Liu
  • Zhenjiang Zhao

Abstract

The impulsive complex‐valued neural networks with three kinds of time delays including leakage delay, discrete delay, and distributed delay are considered. Based on the homeomorphism mapping principle of complex domain, a sufficient condition for the existence and uniqueness of the equilibrium point of the addressed complex‐valued neural networks is proposed in terms of linear matrix inequality (LMI). By constructing appropriate Lyapunov‐Krasovskii functionals, and employing the free weighting matrix method, several delay‐dependent criteria for checking the global μ‐stability of the complex‐valued neural networks are established in LMIs. As direct applications of these results, several criteria on the exponential stability, power‐stability, and log‐stability are obtained. Two examples with simulations are provided to demonstrate the effectiveness of the proposed criteria.

Suggested Citation

  • Xiaofeng Chen & Qiankun Song & Yurong Liu & Zhenjiang Zhao, 2014. "Global μ‐Stability of Impulsive Complex‐Valued Neural Networks with Leakage Delay and Mixed Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:397532
    DOI: 10.1155/2014/397532
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    References listed on IDEAS

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    1. Ting Lei & Qiankun Song & Zhenjiang Zhao & Jianxi Yang, 2013. "Synchronization of Chaotic Neural Networks with Leakage Delay and Mixed Time‐Varying Delays via Sampled‐Data Control," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Ting Lei & Qiankun Song & Zhenjiang Zhao & Jianxi Yang, 2013. "Synchronization of Chaotic Neural Networks with Leakage Delay and Mixed Time-Varying Delays via Sampled-Data Control," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-10, November.
    3. W. Weera & P. Niamsup, 2012. "Exponential Stabilization of Neutral-Type Neural Networks with Interval Nondifferentiable and Distributed Time-Varying Delays," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-21, March.
    4. Liu, Xiwei & Chen, Tianping, 2008. "Robust μ -stability for uncertain stochastic neural networks with unbounded time-varying delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(12), pages 2952-2962.
    5. Yangjun Pei & Chao Liu & Qi Han, 2014. "Stability of Delayed Hopfield Neural Networks with Variable-Time Impulses," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-6, September.
    6. W. Weera & P. Niamsup, 2012. "Exponential Stabilization of Neutral‐Type Neural Networks with Interval Nondifferentiable and Distributed Time‐Varying Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
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    Cited by:

    1. Li, Qiang & Wei, Hanqing & Abdurahman, Abdujelil & Yao, Yangang & Zheng, Yuanshi, 2025. "Dynamic event-triggered H∞ control for T-S fuzzy switched complex-valued networks under average dwell-time constraint: A non-separation approach," Chaos, Solitons & Fractals, Elsevier, vol. 199(P3).

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