Question

Explain in brief procedure for calculating Relative Gain Array for $2\times 2$ systems.

Answer 1

The array R(s) is defined as the element-by-element product (the Hadamard or Schur product) of the transfer-function matrix G(s) and the transpose of the inverse of this matrix, G-T(s)=(GT(s))-1=(G-1(s))T. For non-square systems, that is, systems where the number of inputs does not equal the number of outputs, the pseudo-inverse of G(s) is used, in place of the inverse (Glad and Ljung (2000)). Typically, the relative gain array is evaluated at zero frequency, that is,