A new adaptive parameter update law is proposed for discrete-time model reference adaptive control to ensure robustness with respect to l(1+alpha) (1 less than or equal to alpha less than or equal to infinity) parameter variations and disturbances in the sense that all closed-loop signals are bounded and the tracking error belongs to l(1+alpha) (alpha less than or equal to <(alpha)over bar> infinity) and converges to zero asymptotically.