# ss2tf

Converts state-space model parameters to transfer function model parameters.

## Syntax

[NUM, DEN] = ss2tf(A, B, C, D)

[NUM, DEN] = ss2tf(A, B, C, D, K)

## Inputs

A
The state matrix (n x n), where n is the number of states.
B
The input matrix (n x p), where p is the number of inputs.
C
The output matrix (q x n), where q is the number of outputs.
D
The direct transmission matrix (q x p).
K (optional)
Scalar to extract results for input K. Default: 1.

## Outputs

NUM
The numerator polynomial coefficient vector(s).
DEN
The denominator polynomial coefficient vector.

## Examples

SISO case:
sys_tf = tf([1],[1 3 4]);
sys = ss(sys_tf);
[tf_num,tf_den] = ss2tf(sys.a,sys.b,sys.c,sys.d)
num = [Matrix] 1 x 2
4.44089e-16  1.00000e+00
den = [Matrix] 1 x 3
1.00000  3.00000  4.00000
MIMO case with two outputs and three inputs, selecting input 2:
A = [0.9,0,0.6,-1.4,-4.2;
0.2,0.1,-0.2,0.5,0.6;
-4.3,0,2.2,0,2.4;
-3.7,-0.5,2.4,-0.6,2.7;
6.4,0.1,-4,-0.5,-4];

B = [-0.1,-0.1,0;
0,0,0.1;
-0.1,0.2,-0.1;
0.2,0.2,-0.6;
0.2,-0.1,0.1];

C = [2,7,-2,5,1;
0,-1,3,0,2];

D = [1,0,0;
0,0,0];

[num, den] = ss2tf(A, B, C, D, 2)
num = [Matrix] 2 x 5
0.30000  0.52000  8.02400  14.23650   3.95450
0.40000  0.19000  9.73500   5.46010  -0.09758
den = [Matrix] 1 x 6
1.00000  1.40000  25.39000  35.10400  15.45680  -0.62960

[NUM, DEN] = ss2tf(A, B, C, D, K) returns the transfer function from the K-th input.

Vector DEN contains the denominator coefficients in descending powers of s.

The numerator coefficients are returned in NUM with as many rows as there are outputs.

Transfer function coefficients are stored in descending powers of s or z.

ss2tf does not support multiple input systems. For MIMO support, see ss2tfc.