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tf2ss
Transfer function to state-space conversion.
[A,B,C,D] = tf2ss(num,den)
tf2ss converts a transfer function representation of a given system to an equivalent state-space representation.
[A,B,C,D] = tf2ss(num,den)
finds a state-space representation:
given a system in transfer function form:
from a single input. Input vector den contains the denominator coefficients in descending powers of s. Array num contains the numerator coefficients with as many rows as there are outputs y. tf2ss returns the A, B, C, and D matrices in controller canonical form.
tf2ss also works for discrete systems, but you must pad the numerator with trailing zeros to make it the same length as the denominator.
The function ss2tf is the inverse of tf2ss.
Consider the system
To convert this system to state-space:
num = [0 2 3; 1 2 1];
den = [ 1 0.4 1];
[A,B,C,D] = tf2ss(num,den)
A =
-0.4000 -1.0000
1.0000 0
B =
1
0
C =
2.0000 3.0000
1.6000 0
D =
0
1
There is disagreement in the literature on naming conventions for the canonical forms. It is easy, however, to generate similarity transformations that convert to other forms. For example:
T = fliplr(eye(n));
A = T\A*T;
tf2ss writes the output in controller canonical form by inspection.