How do I use tf2ss() with discrete-time systems?

Question

A have a discrete time transfer function,

H(z^-1) = B(z^-1) / A(z^-1) = (b₀ + b₁z^-1) / (a₀ + a₁z^-1 + a₂z^-2).

whose numerator and denominator are represented in the code as:

Num = [b₀, b₁];
Den = [a₀, a₁, a₂];
T_s = 0.01; % Sampling period`

How do I use tf2ss() to obtain the A, B, C and D state space matrices?
Do I directly call tf2ss() like we do in continuous time system?
Or is there any other built-in Matlab function for this purpose?

Answer 1

Maybe I'm missing something in your question, but you can use it simply like this:

[A, B, C, D] = tf2ss(Den, Num);

You can also refer to the official tf2ss documentation to confirm this.

Answer 2

first of all you should build your continuous state space model by using this: sys_state_space = tf2ss(a,b) after that you should use this: sys_ss_discrete = c2d(sys_state_space,T*-sampling*,'zoh')

then you have the state space discrete model of the system.

Answer 3

Transfer functions to state space conversions are equal in continuous and discrete models. But, if you want the matrices in a system represented discretely you might want to do something like this

S = ss(tf(Num,Den,T))