Feedin vector in feedback function for mimo systems

The documentation for the feedback function shows the following graph to indicate the connections between the plant and the controller.

From the figure, i assume that the feedin vector should be feedin=[4,2] because the 4th input of the plant is connected to the first ouput of the controller and the 2nd input of the plant to the 2nd output of the controller. But in the documentation they do feedin=[2 4]. In the example they shown random state space so only god knows if the result is as expected... Can anyone confirm the correct use of this function in a MIMO system?

Answer 1

[Paul]

Try an example with a known solution.

A = -diag(1:4); B = eye(4); C = eye(4); D = zeros(4);
sysp = ss(A,B,C,D);
sysk = ss(diag([5 10]));
feedout = [2 4];
feedin  = [2 4];
sysc = feedback(sysp,sysk,feedin,feedout,-1);
tf(sysc)

ans =
 
  From input 1 to output...
         1
   1:  -----
       s + 1
 
   2:  0
 
   3:  0
 
   4:  0
 
  From input 2 to output...
   1:  0
 
         1
   2:  -----
       s + 7
 
   3:  0
 
   4:  0
 
  From input 3 to output...
   1:  0
 
   2:  0
 
         1
   3:  -----
       s + 3
 
   4:  0
 
  From input 4 to output...
   1:  0
 
   2:  0
 
   3:  0
 
         1
   4:  ------
       s + 14
 
Continuous-time transfer function.

As you expected, the first output of sysk is mapped to the feedin(1) input to sysp and the second output of sysk is mapped to the feedin(2) input to sysp.

[Roberto Echeverria]

Thank you very much for the confirmation Paul

Regards

Roberto