This paper presents the design of a robust direct model reference adaptive control (DMRAC) algorithm with focus on the satisfaction of an almost strictly positive real (ASPR) condition in the presence of plant uncertainty represented as either variations in plant parameters or unmodelled dynamics in the form of additive or multiplicative norm bounded perturbations in the transfer function. Both the time and frequency domain design conditions for a feedforward compensator have been developed utilizing the robust stability analysis and optimization methods. Illustrative examples are presented to validate the algorithm's use and applicability to control systems with parametric uncertainty or unmodelled dynamics.