Forward Euler Solutions and Weakly Invariant Time-Delayed Systems

Authors

Norma L. Ortiz-Robinson, Virginia Commonwealth UniversityFollow
Vinicio R. Ríos, Universidad del Zulia

Document Type

Article

Original Publication Date

2012

Journal/Book/Conference Title

Abstract and Applied Analysis

Volume

2012

Issue

Article ID 481853, 15 pages

DOI of Original Publication

10.1155/2012/481853

Comments

Originally published at http://dx.doi.org/10.1155/2012/481853

Date of Submission

August 2014

Abstract

This paper presents a necessary and sufficient condition for the weak invariance property of a time-delayed system parametrized by a differential inclusion. The aforementioned condition generalizes the well-known Hamilton-Jacobi inequality that characterizes weakly invariant systems in the nondelay setting. The forward Euler approximation scheme used in the theory of discontinuous differential equations is extended to the time-delayed context by incorporating the delay and tail functions featuring the dynamics. Accordingly, an existence theorem of weakly invariant trajectories is established under the extended forward Euler approach.

Rights

Copyright © 2012 Norma L. Ortiz-Robinson and Vinicio R. Ríos. 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.

Is Part Of

VCU Mathematics and Applied Mathematics Publications