Journal of the
Korean Mathematical Society JKMS

In this paper we develop useful relations which estimate the difference between the solutions of nonlinear impulsive differential systems with different initial values. Then we obtain the converse $h$-stability theorem of Massera's type for the nonlinear impulsive systems by employing the $t_\infty$-similarity of the associated impulsive variational systems and relations.

Keywords: impulsive variational systems, $h$-stability, impulsive differential systems, $t_\infty$-similarity, converse stability theorem

MSC numbers: 34A37, 34D20