Journal of Applied Mathematics and Stochastic Analysis
Volume 8 (1995), Issue 3, Pages 233-247
Razumikhin's method in the qualitative theory of processes with delay
Moscow State University of Communications, Department of Mathematics, Obraztsova St. 15, Moscow 101475, Russia
Received 1 January 1995; Revised 1 March 1995
Copyright © 1995 Anatoly D. Myshkis. 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.
B.S. Razumikhin's concept in the qualitative theory of systems delay is
clarified and discussed. Various ways of improvements of stability conditions are
considered. The author shows that the guiding role of Lyapunov functions and
demonstrates Razumikhin's method as a practical case of continuous version of
the mathematical induction. Several examples demonstrate the obtained results.