Duality properties of linear impulsive systems

Reachability and observability properties of linear switched, impulsive, and switched/impulsive systems have received a great deal of attention over the past decade. The purpose of this paper is to rigorously establish a duality between reachability and observability for linear impulsive systems both in direct system-theoretic terms as well as in geometric terms. These connections are established using an appropriately defined adjoint system associated with the original impulsive system. The duality between reachability and observability is then used to leverage recent reachability results in order to tighten the relationship between the set of unobservable states and a certain invariant subspace.