# TF2SS

## Purpose:

Converts a system in transfer function form to state-space form.

## Syntax:

(A, B, C, D) = TF2SS(num,
den)

num |
- |
A matrix, the numerator coefficients in descending
powers of *s* with as many rows
as there are outputs. |

den |
- |
A series, the denominator coefficients in
descending powers of *s*. |

## Returns:

Matrices A,
B, C, D
of the state space transformation in controller canonical form.

## Example:

For the system:

num = {{0, 1, 3},

{1,
1, 10}};

den = {1, 0.1, 1};

(A, B, C, D) = tf2ss(num, den);

A == {{-0.1, -1.0},

{
1.0, 0.0}}

B == {1.0, 0.0}

C == {{1.0, 3.0},

{0.9,
9.0}}

D == {0.0, 1.0}

## Remarks:

TF2SS converts a system specified in transfer function form to an equivalent
state-space matrix representation such that a single input, multiple output
transfer function:

is converted to state-space form:

where A,
B, C, D
are the matrices of the state space transformation in controller canonical
form:

The conversion also works for discrete systems. For discrete systems,
the input coefficients represent the system:

When specifying a discrete systems, pad the numerator and/or denominator
with zeros to make them the same length.

## See Also:

BILINEAR

FILTEQ

TF2CAS

TF2SOS

TF2ZP

TF2ZPK