Generic Delay-L Left Invertibility of Structured Systems with Scalar Unknown Input

This paper concerns structured systems, namely linear systems where the state-space matrices have zeros in some fixed positions, and free parameters in all other entries. In particular, it focuses on discrete-time linear time-invariant systems affected by an unknown input. The goal is to study delay-L left invertibility, namely the possibility to reconstruct the input sequence from the output sequence, assuming that the initial state is known, and requiring that the inputs can be reconstructed at least up to L time steps before the current output. Under the assumption that the unknown input is scalar, this paper presents a simple graphical condition characterizing the structured systems which are generically delay-L left invertible.