Exercise 3.4 In Figure  what transfer function does SI represent Evaluate the transfer functions from d and d
to r
y

The following relationships are useful

I  L

 LI  L

 S  T  I  

GI KG

 I  GK

G  

GKI  GK

 GI KG

K  I  GK

GK  

T  LI  L

 I  L



 

Note that the matrices G and K in  
  need not be square whereas L  GK is square   follows trivially by factorizing out the term I L

from the right   says that GSI  SG and follows from the push
through rule   also follows from the push
through rule   can be derived from the identity M

M

  MM