How can I obtain the matrices A, B, C ,D of the state space for a transfer matrix using Matlab?

Suppose I have a transfer matrix:

how can I obtain the matrices A, B, C ,D of the state space for this matrix using Matlab?

Answer 1

[Star Strider]

Try this:

s = tf('s');
P = [2/(s^2+3*s+2) 2*s/(s^2+3*s+2); -2*s/(s^2+3*s+2) -2/(s^2+3*s+2)]
S = ss(P)

producing:

S =
 
  A = 
       x1  x2  x3  x4
   x1  -3  -2   0   0
   x2   1   0   0   0
   x3   0   0  -3  -2
   x4   0   0   1   0
 
  B = 
       u1  u2
   x1   2   0
   x2   0   0
   x3   0   2
   x4   0   0
 
  C = 
       x1  x2  x3  x4
   y1   0   1   1   0
   y2  -1   0   0  -1
 
  D = 
       u1  u2
   y1   0   0
   y2   0   0
 
Continuous-time state-space model.

[Flavio Clarizia]

Thanks for answering. Is there a way of doing somehing like:

[A,B,C,D] = ss(P)

so that then I can use these matrices?

Thanks in advance.

[Star Strider]

My pleasure.

The ‘S’ variable is a structure. (See: Access Data in Structure Array for details.)

To get them as arrays:

A = S.A
B = S.B
C = S.C
D = S.D

producing:

A =
    -3    -2     0     0
     1     0     0     0
     0     0    -3    -2
     0     0     1     0

B =
     2     0
     0     0
     0     2
     0     0

C =
     0     1     1     0
    -1     0     0    -1

D =
     0     0
     0     0

All of these are double-precision arrays.

[Flavio Clarizia]

Thank you again. I am trying to apply this to solve this problem :

https://www.mathworks.com/matlabcentral/answers/504811-how-do-i-find-the-the-zero-state-diretion-and-the-zero-input-direction-of-a-transfer-matrix-in-matla?s_tid=prof_contriblnk

I don't know if it is ok to ask here, but could you give it a check if it is not a problem? Thanks in advance.

[Star Strider]

As always, my pleasure!

I posted an Answer to your other Question (that you referenced in your last Comment) that reproduces the anslysis at the end of that monograph. The appropriate MATLAB code is already written, so that was straightforward. (I have not done anything with Rosenbrock System Matrices since my multivariable control course in graduate school, so this was an interesting problem.)