Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics and Stochastic Analysis
Volume 11 (1998), Issue 2, Pages 209-216
http://dx.doi.org/10.1155/S104895339800015X

Second method of Lyapunov for stability of linear impulsive differential-difference equations with variable impulsive perturbations

1Higher Medical Institute, P.O. Box 45, Sofia 1504, Bulgaria
2Technical University, Sliven, Bulgaria
3University of Southwestern Louisiana, Department of Mathematics, P.O. Box 41010, Lafayette, LA 70504, USA

Received 1 May 1996; Revised 1 June 1997

Copyright © 1998 Hindawi Publishing Corporation. 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 present work is devoted to the study of stability of the zero solution to linear impulsive differential-difference equations with variable impulsive perturbations. With the aid of piecewise continuous auxiliary functions, which are generalizations of the classical Lyapunov's functions, sufficient conditions are found for the uniform stability and uniform asymptotical stability of the zero solution to equations under consideration.