We propose a design method for finite-dimensional decentralized VS-MRAC of a class of large-scale non-linear interconnected distributed parameter systems with bounded input and output disturbances. Each equivalent control is approximated by each average control and the norm of the output error vector can be made asymptotically arbitrarily small without the ℳ-matrix condition, independently of the reference inputs and in spite of the presence of non-linear interconnections, unmodelled dynamics and disturbances. Furthermore, it is assured that all signals in the closed-loop system are globally ultimately uniformly bounded. Finally, we show the effectiveness of the proposed method by using a numerical example.