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

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 so...

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Bibliographic Details
Published in:Journal of optimization theory and applications 2018-04, Vol.177 (1), p.261-270
Main Authors: Li, Jin-dong, Huang, Nan-jing
Format: Article
Language:English
Subjects:
Applications of Mathematics
Calculus of Variations and Optimal Control
Optimization
Economic models
Engineering
Mathematical analysis
Mathematics
Mathematics and Statistics
Matrix methods
Neural networks
Operations Research/Decision Theory
Optimization
Stability
Theory of Computation
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Summary: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.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-018-1252-2