tf2ss not returning the correct State Space form

I want to obtain the state space form of the following transfer function using tf2ss:

I went ahead and obtained the state space represention by hand:

So the code I developed to get the state space matrices for the transfer function was:

NUM = [1];
DEN = [1 -1 10];

[A,B,C,D] = tf2ss(NUM,DEN);

The state space matrices returned were:

A = [1 -10 ; 1 0]
B = [1 ; 0]
C = [0 1]
D = 0

It seems to have computed the correct numbers, but they are in the incorrect locations. How do I ensure that tf2ss returns the correct state space matrix representation?

Answer 1

[Star Strider]

The result is correct. The exact configuration doesn’t matter, so long as all the matrices and vectors work together (and produce the correct result).

It may be possible to create a transformation matrix of some sort, however it’s likely not worth the effort. (For what it’s worth, the Control System Toolbox produces a result analogous to the Signal Processing Toolbox that you are using here, except for normalising it.)