MATLAB: Convert a transfer function to controllable and observable canonical form

Question

Hi, I want to convert a transfer function to controllable and observable canonical form for the

num = [4];
den = [1 0.8 4];
Gp = tf (num , den)
Gp =
 
         4
  ---------------
  s^2 + 0.8 s + 4

Answer 1

num = [4];
den = [1 0.8 4];
Gp = tf (num , den);

The canon function requesting the 'companion' canonical form directly produces the observable canonical form:

GpssObs = canon(Gp,'companion')
GpssObsA = GpssObs.A
GpssObsB = GpssObs.B
GpssObsC = GpssObs.C
GpssObsD = GpssObs.D

producing:

GpssObsA =
            0           -4
            1         -0.8
GpssObsB =
     1
     0
GpssObsC =
     0     4
GpssObsD =
     0

The controllable canonical form is then:

GpssConA = GpssObsA.'
GpssConB = GpssObsC.'
GpssConC = GpssObsB.'
GpssConD = GpssObsD

producing:

GpssConA =
            0            1
           -4         -0.8
GpssConB =
     0
     4
GpssConC =
     1     0
GpssConD =
     0

Se the documentation section on: Canonical State-Space Realizations for a full discussion.