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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.

    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.

Examples

expand all

State-Space Representation of Transfer Function

Consider the system described by the transfer function

$$
H(s)=\frac{\left[\begin{array}{c}2s+3\\s^2+2s+1\end{array}\right]}
       {s^2+0.4s+1}.
$$

Convert it to state-space form using tf2ss.

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

See Also

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