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:

$image\tf2ss02.gif$

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:

$image\tf2ss01.gif$

is converted to state-space form:

$image\bilinear05.gif$

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:

$image\zplane03.gif$