The software generates `N`

perturbations
of the identified model `sys`

and then simulates
the response of each of these perturbations. The parameters of the
perturbed realizations of `sys`

are consistent
with the parameter covariance of the original model `sys`

.
The parameter covariance of `sys`

gives information
about the distribution of the parameters. However, for some parameter
values, the resulting perturbed systems can be unstable. To reduce
the probability of generation of unrealistic systems, the software
prescales the parameter covariance.

If *Δp* is the parameter covariance for
the parameters *p* of `sys`

, then
the simulated output *f(p+Δp)* of a perturbed
model as a first-order approximation is:

The `simsd`

command first scales *Δp* by
a scaling factor *s* (approximately 0.1%) to generate
perturbed systems with parameters *(p+sΔp)*.
The command then computes *f(p+sΔp)*, the simulated
response of these perturbed systems. Where,

The command then computes the simulated response *f(p+Δp)* as:

### Note

This scaling is not applied to the free delays of `idproc`

or `idtf`

models.

If you specify the `AddNoise`

option of `simsdOptions`

as `true`

,
the software adds different realizations of the noise sequence to
the noise-free responses of the perturbed system. The realizations
of the noise sequence are consistent with the noise component of the
model.

For state-space models, if you specify the covariance of initial
state values in `X0Covariance`

option of `simsdOptions`

,
different realizations of the initial states are used to simulate
each perturbed model. Initial states are drawn from a Gaussian distribution
with mean `InitialCondition`

and covariance `X0Covariance`

.