Relative gain, multivariable control

Interaction among control loops in a multivariable system has been the subject of much research over the last 20 years. Various types of decouplers were explored to separate the loops. Rosenbrock presented the inverse Nyquist array (INA) to quantify the amount of interaction. Bristol, Shinskey, and McAvoy developed the relative gain array (RGA) as an index of loop interaction... 

Therefore, the following discussions of the relative gain array (RGA) and decoupling are quite brief We include them not because they are all that useful, but because they are part of the history of multivariable control. You should be aware of what they are and what their limitations are so that when you see them being misapplied (which, unfortunately, occurs quite often) you can be knowledgeably skeptical of the conclusions drawn. 

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