How do I convert descriptor state-space to transfer function?

Hello. I have a state-space forumla of the form .

I'd like to have MATLAB convert this into its respective transfer function for me. I plan on encoding

sys = dss(A,B,C,D,E)

However, I looked on the page for transfer functions through tf, and I am unable to find how to convert from this dss to tf. Is there a direct way to encode it? Yes, I know that I can just do it by hand and encode the result myself. I'd just like to know if MATLAB can do it, and if so, how.

https://www.mathworks.com/help/control/ref/dss.html

https://www.mathworks.com/help/control/ref/tf.html

• Thank you

Answer 1

[Star Strider]

This seems to work:

A = [1 2; 3 4];
B = [5; 6];
C = [7 8; 9 10];
D = 0;
E = [11 12; 13 14];

ss_sys = dss(A,B,C,D,E)

ss_sys =
 
  A = 
       x1  x2
   x1   1   2
   x2   3   4
 
  B = 
       u1
   x1   5
   x2   6
 
  C = 
       x1  x2
   y1   7   8
   y2   9  10
 
  D = 
       u1
   y1   0
   y2   0
 
  E = 
       x1  x2
   x1  11  12
   x2  13  14
 
Continuous-time state-space model.

tf_sys = tf(ss_sys)

tf_sys =
 
  From input to output...
          3 s - 8
   1:  -------------
       s^2 - 2 s + 1
 
          4 s - 9
   2:  -------------
       s^2 - 2 s + 1
 
Continuous-time transfer function.

.

[Justin Burzachiello]

Thank you, Star. I appreciate the included code.

[Justin Burzachiello]

Also, do you by any chance know what to do if sparse A,B,C,D,E matrices are so large that I recieve a "unable to convert the model to a transfer function because of overflow" error when using this method?

This is a bit off-topic, so I asked this in a new question, but I thought that I might as well ask here.

[Star Strider]

As always, my pleasure!

Not off-topic at all. I’ve never encountered a similar situation, so I have no idea.

Answer 2

[Jesús Zambrano]

I think you can just take the A,B,C,D matrices and use ss2tf command to convert it to transfer function.

Please look at this documentation which also shows an example:

https://se.mathworks.com/help/matlab/ref/ss2tf.html

Hope it helps!

[Paul]

The E matrix can be ignored?

[Jesús Zambrano]

Oh!, my mistake. I didn’t read the E matrix, sorry. Please see answer below that seems to answer your question.

[Justin Burzachiello]

It's okay, Jesús. Thank you for answering.