Conditioned invariant subspaces for linear impulsive systems

In this paper, conditioned invariant subspaces for a class of linear impulsive systems are investigated. Following the geometric theory for linear time-invariant systems, conditioned invariant subspaces are defined in terms of the existence of an impulsive observer that maintains estimates of the state modulo the given subspace. Geometric conditions are developed that are necessary as well as sufficient for a subspace to be conditioned invariant. These conditions reflect the asymmetric roles played by the continuous-time and discrete-time (impulsive) dynamics that together form the overall impulsive system dynamics.