Exponential and Non-exponential Convergence of Solutions in Some Classes of Nonlinear Systems
by
Jito Vanualailai
University of the South Pacific, Suva, FIJI

Motivated by recent applications of the Lyapunov method in neural networks, which could be considered as dynamical systems for which the convergence of system trajectories to equilibrium states is a necessity, we re-look at a well-known Krasovkii stability criterion pertaining to autonomous systems and then essentially use the same underlying idea to propose appropriate exponential and non-exponential convergence criteria for autonomous and nonautonomous systems. We then apply the criteria to neural networks and discuss our results with respect to recent ones in the field.

Date received: October 1, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cahf-12.