The author considers systems in a Hilbert space governed by impulsive differential inclusions of the form
where is the infinitesimal generator of a -semigroup, and the ’s are multivalued, and . The ’s being set-valued allow for systems in which the jump sizes are uncertain and also problems in which the jump sizes are chosen from a control set. The existence of solutions is proven under the assumptions is closed convex-valued, satisfies a growth condition and is upper semicontinuous; the ’s are closed bounded-valued and map closed and bounded sets into closed and bounded sets; plus several other conditions. Under the additional assumption that the semigroup generated by is compact, the attainable set is characterized. Special cases of this problem in which or the ’s are singleton-valued are also considered. Finally, the author mentions several open questions in control theory relating to these results.