Table of Contents
ISRN Applied Mathematics
Volume 2011, Article ID 145801, 12 pages
Research Article

Lyapunov Stability Analysis of Gradient Descent-Learning Algorithm in Network Training

Mechanical Agriculture Department, Tarbiat Modares University, Tehran, P.O. Box 14115-336, Iran

Received 17 March 2011; Accepted 13 May 2011

Academic Editors: J.-J. Ruckmann and L. Simoni

Copyright © 2011 Ahmad Banakar. 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.


The Lyapunov stability theorem is applied to guarantee the convergence and stability of the learning algorithm for several networks. Gradient descent learning algorithm and its developed algorithms are one of the most useful learning algorithms in developing the networks. To guarantee the stability and convergence of the learning process, the upper bound of the learning rates should be investigated. Here, the Lyapunov stability theorem was developed and applied to several networks in order to guaranty the stability of the learning algorithm.