# 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

```
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
```

```
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
```

## Comments

[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.