Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 78, pp. 1-18.

Title: Lyapunov stability of closed sets in impulsive semidynamical systems
       
Authors: Everaldo M. Bonotto (Univ. de Sao Paulo, Sao Carlos SP, Brazil)
         Nivaldo G. Grulha Jr. (Univ. de Sao Paulo, Sao Carlos SP, Brazil)

Abstract:
  In this article, we consider impulsive semidynamical systems,
 defined in a metric space, with impulse effects at variable times.
 Converse-type theorems are included in our results giving necessary
 and sufficient conditions for various types of stability of
 closed subsets of the metric space.
 These results are achieved  by means of Lyapunov functionals
 which indicate how the solutions behave when entering a
 "stable" set.

Submitted September 8, 2009. Published June 08, 2010.
Math Subject Classifications: 34A37, 37B25, 54H20.
Key Words: Impulsive semidynamical systems; stability; Lyapunov functionals.