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Discrete Dynamics in Nature and Society
Volume 2017 (2017), Article ID 5073640, 10 pages
https://doi.org/10.1155/2017/5073640
Research Article

Robust Linear Neural Network for Constrained Quadratic Optimization

1School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing 102209, China
2Department of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China
3School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650500, China

Correspondence should be addressed to Zixin Liu; moc.361@509nixnix

Received 11 April 2017; Revised 21 July 2017; Accepted 26 July 2017; Published 28 August 2017

Academic Editor: Manuel De la Sen

Copyright © 2017 Zixin Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Based on the feature of projection operator under box constraint, by using convex analysis method, this paper proposed three robust linear systems to solve a class of quadratic optimization problems. Utilizing linear matrix inequality (LMI) technique, eigenvalue perturbation theory, Lyapunov-Razumikhin method, and LaSalle’s invariance principle, some stable criteria for the related models are also established. Compared with previous criteria derived in the literature cited herein, the stable criteria established in this paper are less conservative and more practicable. Finally, a numerical simulation example and an application example in compressed sensing problem are also given to illustrate the validity of the criteria established in this paper.