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

---

Order a Hardcopy of Introduction to Digital Filters

Previous: A Short-Cut to Controller Canonical Form
Next: State Space Simulation in Matlab

---

written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.