The main objective of this paper is to propose a discrete-time model reference robust adaptive control system of a plant in the presence of bounded disturbances. This adaptive control system has a new robust adaptive law whose features are: one is that it belongs to the category of leaky integration method with multiple regularization parameters. It is shown how to theoretically determine these regularization parameters which are regarded as σ in the extended σ-modification to multiple parameters. Furthermore it is one of techniques to assure persistent excitation regardless of the size of disturbances. The other is that, upper bound of disturbances is not necessary to be known a priori to design the adaptive control system.