Geometric methods for unknown-state, unknown-input reconstruction in discrete-time nonminimum-phase systems with feedthrough terms

Unknown-state, unknown-input reconstruction in systems with invariant zeros is intrinsically limited by the fact that, for any invariant zero, at least one initial state exists, s.t. when the mode of the invariant zero is suitably injected into the system, the output remains identically equal to zero. Nonetheless, the problem has recently attracted considerable interest, mainly due to its connections with fault diagnosis and fault tolerant issues. This paper discusses the synthesis of a system capable of reconstructing the generic initial state and the generic bounded input in discrete-time nonminimum-phase linear systems with feedthrough terms. The procedure described is developed within the geometric approach.