Autonomous dissipative semidynamical systems with impulses

Abstract

In the present paper, we study the theory of dissipative impulsive semidynamical systems. We define different types of dissipativity as point, compact, local and bounded. The center of Levinson is defined for compact dissipative impulsive semidynamical systems and its topological properties are investigated. Also, we present results giving necessary and sufficient conditions to obtain dissipativity, and we include some examples to point out that the concepts of the different kinds of dissipativity are not equivalent in general.