Controlled and Conditioned Invariants for Linear Impulsive Systems

Linear impulsive systems are 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. Our aim is to extend the geometric control theory for linear time invariant systems to this system class. In this paper we define controlled invariant and conditioned invariant subspaces for linear impulsive systems with time-driven impulses and establish compensator synthesis results and accompanying connections with closed-loop invariant subspaces. We apply these results to the solution of an output regulation problem with disturbance decoupling for linear impulsive systems