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A new type of recurrent neural networks for real-time solution of Lyapunov equation with time-varying coefficient matrices

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  • Yi, Chenfu
  • Zhang, Yunong
  • Guo, Dongsheng

Abstract

A new kind of recurrent neural network is presented for solving the Lyapunov equation with time-varying coefficient matrices. Different from other neural-computation approaches, the neural network is developed by following Zhang et al.'s design method, which is capable of solving the time-varying Lyapunov equation. The resultant Zhang neural network (ZNN) with implicit dynamics could globally exponentially converge to the exact time-varying solution of such a Lyapunov equation. Computer-simulation results substantiate that the proposed recurrent neural network could achieve much superior performance on solving the Lyapunov equation with time-varying coefficient matrices, as compared to conventional gradient-based neural networks (GNN).

Suggested Citation

  • Yi, Chenfu & Zhang, Yunong & Guo, Dongsheng, 2013. "A new type of recurrent neural networks for real-time solution of Lyapunov equation with time-varying coefficient matrices," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 92(C), pages 40-52.
    • Handle: RePEc:eee:matcom:v:92:y:2013:i:c:p:40-52
    DOI: 10.1016/j.matcom.2013.04.019
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    References listed on IDEAS

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    1. Yang, Degang & Liao, Xiaofeng & Hu, Chunyan & Wang, Yong, 2009. "New delay-dependent exponential stability criteria of BAM neural networks with time delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(5), pages 1679-1697.
    2. Bouzaouache, Hajer & Braiek, Naceur Benhadj, 2008. "On the stability analysis of nonlinear systems using polynomial Lyapunov functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 76(5), pages 316-329.
    3. Laabidi, Kaouther & Bouani, Faouzi & Ksouri, Mekki, 2008. "Multi-criteria optimization in nonlinear predictive control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 76(5), pages 363-374.
    4. Rotella, F. & Borne, P., 1989. "Explicit solution of Sylvester and Lyapunov equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 31(3), pages 271-281.
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    Cited by:

    1. Bolin Liao & Cheng Hua & Xinwei Cao & Vasilios N. Katsikis & Shuai Li, 2022. "Complex Noise-Resistant Zeroing Neural Network for Computing Complex Time-Dependent Lyapunov Equation," Mathematics, MDPI, vol. 10(15), pages 1-17, August.
    2. Hosseinipour-Mahani, N. & Malek, A., 2016. "A neurodynamic optimization technique based on overestimator and underestimator functions for solving a class of non-convex optimization problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 122(C), pages 20-34.
    3. Zhang, Yunong & Zhai, Keke & Chen, Dechao & Jin, Long & Hu, Chaowei, 2016. "Challenging simulation practice (failure and success) on implicit tracking control of double-integrator system via Zhang-gradient method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 120(C), pages 104-119.

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