Create the following discrete-time transfer function:

H = tf([1 -1],[1 1 0.3],0.1);

The sample time of the model is $$T_s=0.1s$$.

Derive a continuous-time, zero-order-hold equivalent model.

Hc = d2c(H)

Hc =
 
   121.7 s + 2.054e-12
  ---------------------
  s^2 + 12.04 s + 776.7
 
Continuous-time transfer function.

Discretize the resulting model, Hc, with the default zero-order hold method and sample time 0.1s to return the original discrete model, H.

c2d(Hc,0.1)

ans =
 
      z - 1
  -------------
  z^2 + z + 0.3
 
Sample time: 0.1 seconds
Discrete-time transfer function.

Use the Tustin approximation method to convert H to a continuous time model.

Hc2 = d2c(H,'tustin');

Discretize the resulting model, Hc2, to get back the original discrete-time model, H.

c2d(Hc2,0.1,'tustin');

Estimate a discrete-time transfer function model, and convert it to a continuous-time model.

load iddata1
sys1d = tfest(z1,2,'Ts',0.1);
sys1c = d2c(sys1d,'zoh');

Estimate a continuous-time transfer function model.

sys2c = tfest(z1,2);

Compare the response of sys1c and the directly estimated continuous-time model, sys2c.

compare(z1,sys1c,sys2c)

The two systems are almost identical.

Convert an identified discrete-time transfer function model to continuous-time.

load iddata1
sysd = tfest(z1,2,'Ts',0.1);
sysc = d2c(sysd,'zoh');

sys1c has no covariance information. The d2c operation leads to loss of covariance data of identified models.

Regenerate the covariance information using a zero iteration update with the same estimation command and estimation data.

opt = tfestOptions; 
opt.SearchOptions.MaxIterations = 0;
sys1c = tfest(z1,sysc,opt);

Analyze the effect on frequency-response uncertainty.

h = bodeplot(sysd,sys1c);
showConfidence(h,3)

The uncertainties of sys1c and sysd are comparable up to the Nyquist frequency. However, sys1c exhibits large uncertainty in the frequency range for which the estimation data does not provide any information.

If you do not have access to the estimation data, use the translatecov command which is a Gauss-approximation formula based translation of covariance across model type conversion operations.