Mathematical Problems in Engineering
Volume 2008 (2008), Article ID 698043, 10 pages
doi:10.1155/2008/698043
Research Article
Numerical Stability Test of Neutral Delay Differential Equations
Institute of Vibration Engineering Research, Nanjing University of Aeronautics and Astronautics, 210016 Nanjing, China
Received 24 October 2007; Revised 1 March 2008; Accepted 16 March 2008
Academic Editor: Jose Balthazar
Copyright © 2008 Z. H. Wang. 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
The stability of a delay differential equation can be investigated
on the basis of the root location of the characteristic function. Though a number of stability
criteria are available, they usually do not provide any information about the characteristic root
with maximal real part, which is useful in justifying the stability and in understanding the system
performances. Because the characteristic function is a transcendental function that has an infinite
number of roots with no closed form, the roots can be found out numerically only. While some
iterative methods work effectively in finding a root of a nonlinear equation for a properly chosen
initial guess, they do not work in finding the rightmost root directly from the characteristic function.
On the basis of Lambert W function, this paper presents an effective iterative algorithm for the calculation
of the rightmost roots of neutral delay differential equations so that the stability of the delay equations
can be determined directly, illustrated with
two examples.