Linear function dead-beat observers for linear periodic discrete-time systems with unknown disturbances

In this paper the classical notion of conditioned invariant subspace is extended to the case of linear periodic discrete-time systems, properly characterized, and suitably specialized to the notion of outer reconstructible subspace. Both of these notions are used in order to find the necessary and sufficient conditions for the existence of a linear function dead-beat observer for such systems under unknown and unmeasurable disturbances and a synthesis procedure of it.