Time-Varying Complex Matrix Inverse

  • Yunong ZhangEmail author
  • Dongsheng Guo


In this chapter, the ZD approach is further extended and exploited for time-varying matrix inversion in complex domain. Specifically, focusing on time-varying complex matrix inversion, we propose, generalize, develop, and investigate three different complex ZD models by defining three different complex ZFs. Through simulations and verifications with four illustrative examples, the corresponding results substantiate the efficacy of the complex ZD models based on different complex ZFs for time-varying complex matrix inversion.


Time-Varying Matrix Inversion Global Convergence Performance Error-monitoring Function Vectorization Techniques Complex-valued Weight 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Steriti RJ, Fiddy MA (1993) Regularized image reconstruction using SVD and a neural network method for matrix inversion. IEEE Trans Signal Process 41(10):3074–3077CrossRefzbMATHGoogle Scholar
  2. 2.
    Van Huffel S, Vandewalle J (1989) Analysis and properties of the generalized total least squares problem \(AX \approx B\) when some or all columns in \(A\) are subject to error. SIAM J Matrix Anal Appl 10(3):294–315CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Chen M, Ge SS, How BVE (2010) Robust adaptive neural network control for a class of uncertain MIMO nonlinear systems with input nonlinearities. IEEE Trans Neural Netw 21(5):796–812CrossRefGoogle Scholar
  4. 4.
    Liu YJ, Tong S, Li Y (2010) Adaptive neural network tracking control for a class of non-linear systems. Int J Syst Sci 41(2):143–158CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Yang C, Ge SS, Lee TH (2009) Output feedback adaptive control of a class of nonlinear discrete-time systems with unknown control directions. Automatica 45(1):270–276CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Li Z, Xia Y (2013) Adaptive neural network control of bilateral teleoperation with unsymmetrical stochastic delays and unmodeled dynamics. Int J Robust Nonlinear Control 24(11):1628–1652CrossRefMathSciNetGoogle Scholar
  7. 7.
    Zhang Y, Yi C (2011) Zhang neural networks and neural-dynamic method. Nova Science Publishers, New YorkGoogle Scholar
  8. 8.
    Guo D, Zhang Y (2012) Zhang neural network, Getz-Marsden dynamic system, and discrete-time algorithms for time-varying matrix inversion with application to robots’ kinematic control. Neurocomputing 97:22–32CrossRefGoogle Scholar
  9. 9.
    Guo D, Qiu B, Ke Z, Yang Z, Zhang Y (2014) Case study of Zhang matrix inverse for different ZFs leading to different nets. In: Proceedings of the international joint conference on neural networks, pp 2764–2769Google Scholar
  10. 10.
    Wang J (1993) A recurrent neural network for real-time matrix inversion. Appl Math Comput 55(1):89–100CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Zhang Y, Chen K, Tan H (2009) Performance analysis of gradient neural network exploited for online time-varying matrix inversion. IEEE Trans Autom Control 54(8):1940–1945CrossRefMathSciNetGoogle Scholar
  12. 12.
    Zhang Y, Ge SS (2005) Design and analysis of a general recurrent neural network model for time-varying matrix inversion. IEEE Trans Neural Netw 16(6):1477–1490CrossRefGoogle Scholar
  13. 13.
    Getz NH, Marsden JE (1995) A dynamic inverse for nonlinear maps. In: Proceedings of 34th IEEE conference on decision and control, pp 4218–4223Google Scholar
  14. 14.
    Getz NH, Marsden JE (1995) Joint-space tracking of workspace trajectories in continuous time. In: Proceedings of 34th IEEE conference on decision and control, pp 1001–1006Google Scholar
  15. 15.
    Getz NH, Marsden JE (1997) Dynamical methods for polar decomposition and inversion of matrices. Linear Algebra Appl 258:311–343CrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    Song J, Yam Y (1998) Complex recurrent neural network for computing the inverse and pseudo-inverse of the complex matrix. Appl Math Comput 93(2–3):195–205CrossRefzbMATHMathSciNetGoogle Scholar
  17. 17.
    Zhang Y, Li Z, Li K (2011) Complex-valued Zhang neural network for online complex-valued time-varying matrix inversion. Appl Math Comput 217(24):10066–10073CrossRefzbMATHMathSciNetGoogle Scholar
  18. 18.
    Zhang Y, Guo D, Li F (2013) Different complex ZFs leading to different complex ZNN models for time-varying complex matrix inversion. In: Proceedings of 10th IEEE international conference on control and automation, pp 1330–1335Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.School of Information Science and TechnologySun Yat-sen UniversityGuangzhouChina

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