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Asymptotical Stability for a Class of Complex-Valued Projective Neural Network

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Abstract

In this paper, a new class of complex-valued projective neural network is introduced and studied on a nonempty, closed, and convex subset of a finite-dimensional complex space. An existence and uniqueness result for the equilibrium point of complex-valued projective neural network is proved under some suitable conditions. Moreover, by utilizing the linear matrix inequality technique, some sufficient conditions are presented to ensure the asymptotical stability of the complex-valued projective neural network. Finally, two examples are given to illustrate the validity and feasibility of main results.

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Acknowledgements

The authors are grateful to the editor and the referees for their valuable comments and suggestions. This work was supported by the National Natural Science Foundation of China (11471230, 11671282) and the Applied Basic Research Programs of Department of Science and Technology of Sichuan Province of China (No. 2016JY0249).

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Authors and Affiliations

  1. Department of Mathematics, Sichuan University, Chengdu, People’s Republic of China

    Jin-dong Li & Nan-jing Huang

  2. College of Management Science, Chengdu University of Technology, Chengdu, People’s Republic of China

    Jin-dong Li

Authors
  1. Jin-dong Li
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  2. Nan-jing Huang
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Correspondence to Nan-jing Huang.

Additional information

Communicated by Xinmin Yang.

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Li, Jd., Huang, Nj. Asymptotical Stability for a Class of Complex-Valued Projective Neural Network. J Optim Theory Appl 177, 261–270 (2018). https://doi.org/10.1007/s10957-018-1252-2

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  • DOI: https://doi.org/10.1007/s10957-018-1252-2

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