Ed Bristol (a control engineer with Foxboro) developed a heuristic technique to predict possible interactive effects between control loops when multiple SISO loops are used. He was motivated to develop a dimensionless measure of interaction by some boiler control problems he was working on. His simple measure of interaction is known as the relative gain, or the Bristol relative gain array (RGA). Since then, many papers have been written to provide a more rigorous theoretical basis for the technique.
The relationship between u1 and y1 at steady state (s = 0), with no change in u2, is
This is referred to as the gain between u1 and y1 with all other loops open (that is, u