Signal Processing Toolbox

tf2ss

Convert transfer function filter parameters to state-space form.

Syntax

[A,B,C,D] = tf2ss(b,a)

Description

tf2ss converts the parameters of a transfer function representation of a given system to those of an equivalent state-space representation.

[A,B,C,D] = tf2ss(b,a) returns the A, B, C, and D matrices of a state space representation for the single-input transfer function

in controller canonical form

The input vector a contains the denominator coefficients in descending powers of s. The rows of the matrix b contain the vectors of numerator coefficients (each row corresponds to an output). In the discrete-time case, you must supply b and a to correspond to the numerator and denominator polynomials with coefficients in descending powers of z.

For discrete-time systems you must make b have the same number of columns as the length of a. You can do this by padding each numerator represented in b (and possibly the denominator represented in the vector a) with trailing zeros. You can use the function eqtflength to accomplish this if b and a are vectors of unequal lengths.

The tf2ss function is part of the standard MATLAB language.

Example

Consider the system

To convert this system to state-space, type

b = [0 2 3; 1 2 1];
a = [1 0.4 1];
[A,B,C,D] = tf2ss(b,a)
A =
   -0.4000   -1.0000
    1.0000         0
B =
     1
     0
C =
    2.0000    3.0000
    1.6000         0
D =
     0
     1

Note    There is disagreement in the literature on naming conventions for the canonical forms. It is easy, however, to generate similarity transformations that convert these results to other forms.

See Also

sos2ss	Convert a digital filter second-order sections form to state-space form.
ss2tf	Convert state-space filter parameters to transfer function form.
tf2sos	Convert digital filter transfer function parameters to second-order sections form.
tf2zp	Convert transfer function filter parameters to zero-pole-gain form.
zp2ss	Convert zero-pole-gain filter parameters to state-space form.

tf2sos

tf2zp