c2d is used to convert a model from continuous to discrete time. The official doc states:

sysd = c2d(sysc,Ts) discretizes the continuous-time dynamic system model sysc using zero-order hold on the inputs and a sample time of Ts.

Why is it that when I do:

>> c2d(1/s, 1)

I get:

ans =

  z - 1

Sample time: 1 seconds
Discrete-time transfer function.

but according to Z-transform tables the z transform of 1/s is

ans =

  z - 1

Why this discrepancy?

  • 1
    \$\begingroup\$ Probably the integration method. c2d uses the zero order hold by default. Z transform table might use another method. \$\endgroup\$ – Jaywalk Feb 6 at 15:18
  • \$\begingroup\$ The Z-transform table is the result of the backward rectangular rule. \$\endgroup\$ – Suba Thomas Feb 6 at 15:36
sys = c2d (sys, tsam, method)

If you do not include the method it will use zero-order hold


resulting in $$ \frac{1}{z-1} $$

If you pick a different conversion method it gives you different results, but notice that the poles stability will be "conserved"


results in $$ \frac{0.5z+0.5}{z-1} $$


results in $$ \frac{z}{z-1} $$


results in $$ \frac{1.052}{z-1} $$

| improve this answer | |

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.