The command `usample`

is
used to randomly sample an uncertain object, giving a not-uncertain
instance of the uncertain object.

If `A`

is an uncertain object, then `usample(A)`

generates
a single sample of `A`

.

For example, a sample of a `ureal`

is a scalar `double`

.

A = ureal('A',6); B = usample(A) B = 5.7298

Create a 1-by-3 `umat`

with `A`

and
an uncertain complex parameter `C`

. A single sample
of this `umat`

is a 1-by-3 double.

C = ucomplex('C',2+6j); M = [A C A*A]; usample(M) ans = 5.9785 1.4375 + 6.0290i 35.7428

If `A`

is an uncertain object, then `usample(A,N)`

generates `N`

samples
of `A`

.

For example, 20 samples of a `ureal`

gives
a 1-by-1-20 `double`

array.

B = usample(A,20); size(B) ans = 1 1 20

Similarly, 30 samples of the 1-by-3 `umat`

`M`

yields
a 1-by-3-by-30 array.

size(usample(M,30)) ans = 1 3 30

See Create Arrays with usample for more information on sampling uncertain objects.

When sampling an `ultidyn`

element or an uncertain object that contains a `ultidyn`

element, the result is always a state-space (`ss`

) object. The property `SampleStateDim`

of the `ultidyn`

class determines the state dimension of the samples.

Create a 1-by-1, gain bounded `ultidyn`

object with gain bound 3. Verify that the default state dimension for samples is 1.

del = ultidyn('del',[1 1],'Bound',3); del.SampleStateDim

ans = 1

Sample the uncertain element at 30 points. Verify that this creates a 30-by-1 `ss`

array of 1-input, 1-output, 1-state systems.

delS = usample(del,30); size(delS)

30x1 array of state-space models. Each model has 1 outputs, 1 inputs, and 1 states.

Plot the Nyquist plot of these samples and add a disk of radius 3. Note that the gain bound is satisfied and that the Nyquist plots are all circles, indicative of 1st order systems.

nyquist(delS) hold on; theta = linspace(-pi,pi); plot(del.Bound*exp(sqrt(-1)*theta),'r'); hold off;

Change the `SampleStateDim`

to 4, and repeat entire procedure. The Nyquist plots satisfy the gain bound and as expected are more complex than the circles found in the 1st-order sampling.

del.SampleStateDim = 4; delS = usample(del,30); nyquist(delS) hold on; theta = linspace(-pi,pi); plot(del.Bound*exp(sqrt(-1)*theta),'r'); hold off;

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