New Razumikhin-type theorems on the stability for impulsive functional differential systems

In this paper, we investigate the stability of the trivial solution for impulsive functional differential systems using several Lyapunov functions including partial components coupled with the Razumikhin technique, and obtained some new Razumikhin-type theorems which avoid using the auxiliary function P$P$ under less restrictive conditions. Our results improve some of the earlier findings, and are suitable for many applications. Some examples are given to illustrate the advantages of the theorems obtained.