Linear impulsive systems constitute a class of hybrid systems in which the state propagates according to linear continuous-time dynamics except for a countable set of times at which the state can change instantaneously. While in general these impulsive effects can be time-driven and/or event-driven, here we focus our attention on the time-driven case. For this class of systems, we address the fundamental concepts of reachability and observability. In particular, we present a geometric characterization of the reachable and unobservable sets in terms of invariant subspaces and provide algorithms for their construction. (c) 2008 Elsevier Ltd. All rights reserved.