Dead-beat observers of reduced order for linear periodic discrete-time systems with inaccessible inputs

In this paper necessary and sufficient conditions are given for the existence of a dead-beat observer for a linear periodic discrete-time system subject to immeasurable periodic disturbances. The conditions express, in terms of the disturbed system, the reconstructibility of the augmented system obtained by connecting the former with the disturbance generator. A synthesis procedure of the observer is also provided.