Journal of Applied Mathematics and Stochastic Analysis
Volume 11 (1998), Issue 2, Pages 209-216
Second method of Lyapunov for stability of linear impulsive
differential-difference equations with variable impulsive
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 70504, LA, USA
Received 1 May 1996; Revised 1 June 1997
Copyright © 1998 D. D. Bainov et al. 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.
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.