I am trying to design a decoupler to break a MIMO system down to a distributed SISO system for control. I am reading a paper on how to do that, but it is telling me to compute some strange stuff that I am not understanding. Please see the below computations:
How is the second equation computed? The x inside the circle usually represents the tensor product in math literature, so the dimensions of the new matrix should be the multiplication of the size of the two original matrices. Since originally, the matrices are 2x2, the resultant matrix should be 4 x 4. I assume the -T does not represent the inverse of the transpose?
Turns out the x with the circle in it did not represent a tensor product, rather, it represented an element-wise multiplication...
So it is solved by taking the transpose of the inverse of K, and then doing element-wise multiplication.