Matlab Direct-Form to State-Space Conversion

Matlab and Octave support state-space models with functions such as

• tf2ss - transfer-function to state-space conversion
• ss2tf - state-space to transfer-function conversion

Note that while these utilities are documented primarily for use with continuous-time systems, they are also used for discrete-time systems.

Let's repeat the previous example using Matlab:

>> num = [1 2 3]; % transfer function numerator 
>> den = [1 1/2 1/3]; % denominator coefficients
>> [A,B,C,D] = tf2ss(num,den)

A =
   -0.5000   -0.3333
    1.0000         0

B =
     1
     0

C =  1.5000    2.6667

D =  1

>> [N,D] = ss2tf(A,B,C,D)

N = 1.0000    2.0000    3.0000

D = 1.0000    0.5000    0.3333

The tf2ss and ss2tf functions are documented online at The Mathworks help desk as well as within Matlab or Octave itself (say help tf2ss).