MATLAB: Controllable, Observable and Jordan or Diagonal Form from Transfer function

canonicalmatrixstate-space

Hi, I have the following transfer function:

>> num = [2 3];

>> den = [1 3 3 1 0];

>> G = tf(num,den);

I was wondering how to convert the transfer function to specifically in the form of controllable, observable and Jordan?

See the ctrb and obsv functions in the Control System Toolbox. The jordan function is a core MATLAB function.

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.

The tf2ss function wants a transfer function as input, not a system object.

Try this:

[A B C D]=tf2ss(Den,Num)
A =
    -5    -6
     1     0
B =
     1
     0
C =
     1     1
D =
     0

EDIT —

To get the state space representation from a system object, just use the ss funciton:

[A B C D] = ss(s);