  The Relative Gain Array (RGA) and Relative Normalized Gain Array (RNGA) have
received considerable attention for square systems. In this paper RNGA with the
column-major, for non-square multivariable systems is introduced. RNGA of the
paper has a row-column inequality, i.e. the number of rows is less than the
number of columns. Unlike the conventional RGA, the RNGA loop pairing criteria
of the paper considers both steady-state as well as transient information for
the assessment of control-loop interactions. The RNGA for square systems is
extended for non-square multivariable systems by thoroughly deriving its
supporting properties. The RNGA method is applied to a non-square multivariable
radiator laboratory test setup for loop pairing. Closed-loop results arising
from the RNGA-based loop pairing are depicted in the paper. The lacuna of the
conventional RGA loop pairing has been overcome by the application of the
developed RNGA of this paper. The results unfold the effectiveness of RNGA over
RGA for non-square multivariable systems to have minimum interactions and
better control.
