MATLAB: No model detection for a input / output vectors in a MIMO Syetem

Question

How can I determine if a pair of input/output vectors (y and u) have no model for a MIMO transfer function? y and u are i-th and j-th output and input vectors, respectively. I am trying to know if there is not a model for them, in order to put a zero in that position, otherwise a proper system identification method would be used to determine the existing model. Attention: cross correlation analysis between y and u is not enough to determine this. I will appreciate any suggestion.

Answer 1

What do you mean by "no model for a MIMO transfer function"? If you are trying to analyze if j:th output is affected by i:th input or not, you can do some sort of regression analysis (partial least squares, ARX modeling). For each output, you could try a order determination exercise (see ARXSTRUC, SELSTRUC). The optimal orders shown by SELSTRUC would indicate the weights assigned to each input signals towards determination of the output. Note that it may not be easy to isolate the effect of one input signal on a particular output or determine such effects uniquely. However, Principal Component analysis or Partial Least Squares techniques would let you determine a minimal set of inputs that appear to be strongly correlated with the output.