MATLAB: Discrepancy between using function ‘feedback()’ and calculating manually

closed loopControl System Toolboxfeedback

Hello,
I am working with MIMO systems and have made a comparison between the results obtained using the Matlab function 'feedback()' and computing the closed loop transfer function 'by hand'. There are differences between them I don't understand.
The code below illustrates the issue. I define a forward path array of transfer functions G and close the loop with K in the feedback path.
To compute the feedback manually I calculate CL = G/(I+K*G).
If you run this code fragment you will see that 'cl1' and 'cl2' do not agree. I don't understand why not. Can anyone enlighten me please?
Thanks,
Chris
g11 = tf(1,[1 0]);
g12 = tf(2,[1 0]);
g21 = tf(3,[1 0]);
g22 = tf(4,[1 0]);
G = [g11 g12;g21 g22];
k = 2;
K = [k 0;0 0];
cl1 = feedback(G,K,-1)
I = eye(2);
cl2 = G / (I + K*G)

Best Answer

cl2 can be simplfied by canceling s out of the numerator and denominator of each entry. After that you'll see that cl2 and cl1 are the same to within some roundoff. Or are you concerned about the roundoff?