Document Type


Source Publication Title

Technical Report 9


The use of Lyapunov-like vector functions is recognized as an important tool for estimating the behavior of a dynamical system. In applications, one needs to determine a suitable comparison function which contains information or properties that can be used to obtain some information about the behavior of the dynamical system. In recent years, the remarkable property of pointwise degeneracy has been discovered for linear, autonomous, delay-differential equations. For this class of equations one knows that all solutions will reach a subspace in finite time and remain on the subspace thereafter. As this class of equations is particularly simple, it becomes an obvious candidate for use as a comparison function. In this paper (Section 3), we show how one may effectively use pointwise degenerate systems as comparison functions. Section 4 treats functional differential equations which possess certain monotonic features. These monotonic properties do not appear to allow us to select pointwise degenerate systems as natural comparison functions.


Mathematics | Physical Sciences and Mathematics

Publication Date




Included in

Mathematics Commons



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.