We present a direct model reference adaptive controller for discrete-time systems (and thus sampled-data systems) that are possibly nonminimum phase. The adaptive control algorithm requires knowledge of the nonminimumphase zeros of the transfer function from the control to the tracking error. This paper and its companion paper (Part 2)
together analyze the stability of the instantaneous (gradientbased) retrospective cost model reference adaptive controller and the cumulative (recursive-least-squares-based) retrospective cost model reference adaptive controller. Part 1 develops the adaptive controllers and proves the existence of an ideal control law. Part 2 presents the closed-loop error system and provides a closed-loop stability analysis.