Remarks on persistency of excitation for nonminimal models of systems having purely deterministic disturbances

A persistency of excitation result for nonminimal models of systems having purely deterministic disturbances has been given recently in [1]. In this note we give a direct and simple proof for the case of bounded signals of the result of [1] and show, via a counterexample, that an assumption on system signals boundedness which does not appear in [1] is necessary when arbitrary unbounded signals are allowable. Finally, we give a proper persistency of excitation result which does not require signal boundedness for the case when the system input consists of a bounded external signal and of a constant coefficient feedback component.