Comments on a robust model reference adaptive control for non-minimum phase systems with unknown or time-varying delay (Q1614288)

The present note concerns several mathematical mistakes discovered by the author in the paper [\textit{M. Makoudi} and \textit{L. Radouane}, Automatica 36, 1057-1065 (2000; Zbl 0961.93034)]. This paper presented a model reference adaptive control algorithm that is based on a special ``operator'' \(\Pi\), defined as \[ \Pi(\cdot) (t-i)= \alpha(t)^i(t-i),\quad \text{with }0< \alpha(t) <1, \] and devoted to removing the usual non-minimum phase assumption. The author of the present note shows that the ``operator'' \(\Pi\) cannot be used in the way stated and intended by Makoudi and Radouane (loc. cit.), rendering several basic theorems erroneous. Thus the results presented in the referenced paper are questionable.