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.

Keywords

Complex-valued projective neural network Equilibrium point Linear matrix inequality technique Homeomorphism method Asymptotical stability 

Mathematics Subject Classification

49J40 34K20 92B20 

Notes

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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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsSichuan UniversityChengduPeople’s Republic of China
  2. 2.College of Management ScienceChengdu University of TechnologyChengduPeople’s Republic of China

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