State observers for discrete-time linear systems with unknown inputs

In the paper the problem of designing a full-order state observer for a general discrete-time linear system with unknown inputs is analyzed. Necessary and sufficient conditions for the existence either of an asymptotic or of a deadbeat observer are provided, and a constructive design procedure, together with some examples, are discussed. Finally, the equivalence of these conditions for problem solvability with those derived in previous contributions by means of different approaches is explicitly proved.