- Function File:
`s`=**tf**(`'s'`) - Function File:
`z`=**tf**(`'z', tsam`) - Function File:
`sys`=**tf**(`sys`) - Function File:
`sys`=**tf**(`mat, ...`) - Function File:
`sys`=**tf**(`num, den, ...`) - Function File:
`sys`=**tf**(`num, den, tsam, ...`) Create or convert to transfer function model.

**Inputs**`sys`- LTI model to be converted to transfer function.
`mat`- Gain matrix to be converted to static transfer function.
`num`- Numerator or cell of numerators. Each numerator must be a row vector
containing the coefficients of the polynomial in descending powers of
the transfer function variable.
num{i,j} contains the numerator polynomial from input j to output i.
In the SISO case, a single vector is accepted as well.
`den`- Denominator or cell of denominators. Each denominator must be a row vector
containing the coefficients of the polynomial in descending powers of
the transfer function variable.
den{i,j} contains the denominator polynomial from input j to output i.
In the SISO case, a single vector is accepted as well.
`tsam`- Sampling time in seconds. If
`tsam`is not specified, a continuous-time model is assumed. `...`- Optional pairs of properties and values.
Type
`set (tf)`for more information.

**Outputs**`sys`- Transfer function model.

**Option Keys and Values**`'num'`- Numerator. See 'Inputs' for details.
`'den'`- Denominator. See 'Inputs' for details.
`'tfvar'`- String containing the transfer function variable.
`'inv'`- Logical. True for negative powers of the transfer function variable.
`'tsam'`- Sampling time. See 'Inputs' for details.
`'inname'`- The name of the input channels in
`sys`. Cell vector of length m containing strings. Default names are`{'u1', 'u2', ...}`

`'outname'`- The name of the output channels in
`sys`. Cell vector of length p containing strings. Default names are`{'y1', 'y2', ...}`

`'ingroup'`- Struct with input group names as field names and
vectors of input indices as field values.
Default is an empty struct.
`'outgroup'`- Struct with output group names as field names and
vectors of output indices as field values.
Default is an empty struct.
`'name'`- String containing the name of the model.
`'notes'`- String or cell of string containing comments.
`'userdata'`- Any data type.

**Example**octave:1> s = tf ('s'); octave:2> G = 1/(s+1) Transfer function 'G' from input 'u1' to output ... 1 y1: ----- s + 1 Continuous-time model.

octave:3> z = tf ('z', 0.2); octave:4> H = 0.095/(z-0.9) Transfer function 'H' from input 'u1' to output ... 0.095 y1: ------- z - 0.9 Sampling time: 0.2 s Discrete-time model.

octave:5> num = {[1, 5, 7], [1]; [1, 7], [1, 5, 5]}; octave:6> den = {[1, 5, 6], [1, 2]; [1, 8, 6], [1, 3, 2]}; octave:7> sys = tf (num, den)

Transfer function 'sys' from input 'u1' to output ... s^2 + 5 s + 7 y1: ------------- s^2 + 5 s + 6 s + 7 y2: ------------- s^2 + 8 s + 6

Transfer function 'sys' from input 'u2' to output ... 1 y1: ----- s + 2 s^2 + 5 s + 5 y2: ------------- s^2 + 3 s + 2 Continuous-time model. octave:8>

**See also:**filt, ss, dss.

Package: control