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

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 itself (say help tf2ss). In Octave, say help tf2ss or help -i tf2ss.

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