An assumption-free theorem on discrete-time positive real systems

This is the final version. Available on open access from Elsevier via the DOI in this recordIFAC‑V 2020: 1st Virtual IFAC World Congress, 11 - 17 July 2020, Berlin, GermanyThe discrete-time positive real lemma is examined and the assumptions of controllability and observability are removed. An intermediate theorem is proved that removes only the assumption of controllability. This work is intended to be the counterpart - and is inspired by - recent work on the continuous-time positive real lemma, and does not assume asymptotic stability unlike the recent results of Ferrante and Ntogramatzidis (2017)