Disturbance Decoupling with Stability for Linear Impulsive Systems

The paper deals with the problem of decoupling the output of an impulsive linear system from a disturbance input by means of a stabilizing state feedback. Geometric methods are used to characterize the decoupling requirement from a structural point of view and in terms of feedback stabilizability. Assuming that the length of the time intervals between consecutive impulsive variations of the state, or jumps, is lower bounded by a positive constant, necessary and sufficient conditions for the existence of solutions are given and discussed.