Hyers-Ulam-Rassias Stability of Functional Differential Systems with Point and Distributed Delays

M De La Sen

doi:10.1155/2015/492515

Abstract

This paper investigates stability and asymptotic properties of the error with respect to its nominal version of a nonlinear time-varying perturbed functional differential system subject to point, finite-distributed, and Volterra-type distributed delays associated with linear dynamics together with a class of nonlinear delayed dynamics. The boundedness of the error and its asymptotic convergence to zero are investigated with the results being obtained based on the Hyers-Ulam-Rassias analysis.

Highlights

The background literature on Hyers-Ulam-Rassias analysis is abundant and many different problems have been solved with it under the basis that there is a perturbation of a nominal equation and that a norm upper-bounding function of the error is obtained, [1,2,3,4,5,6,7,8,9,10,11,12,13]
We develop a related formal stability analysis of functional differential equations with internal delays under the forms (2)–(6) and satisfying hypotheses (H.1)-(H.2)
An upper-bounding function of generic structure, the supremum of the norm of the state, will be assumed to be known in the formal subsequent developments. This general structure of the functional equation of dynamics and its stability study under the Hyers-Ulam-Rassias formalism are the main contribution of the paper

Summary

Introduction

The background literature on Hyers-Ulam-Rassias analysis is abundant and many different problems have been solved with it under the basis that there is a perturbation of a nominal equation and that a norm upper-bounding function of the error is obtained, [1,2,3,4,5,6,7,8,9,10,11,12,13].

Results

Conclusion