In the similar manner, relative gains between other input-output combinations can be calculated as . The relative gain array is expressed in the matrix form as

(VI.9)

It should be noted that sum of relative gains along any row or column should be 1.

The relative gain provides useful information on interaction

•  If , input does not have any effect on output and thus they should not be paired.

•  If , input does not have any effect on output and hence the system is completely decoupled . Thus pairing of input and output is ideal.

•  If , interaction exists. Smaller the value of relative gain, larger will be the interaction.

•  If , input has strong effect on output and that also in the opposite direction of that of input Here the interaction effect is dangerous an detrimental for the system.