If an uncertain object (`umat`

, `uss`

, `ufrd`

)
has many uncertain parameters, it is often necessary to freeze some,
but not all, of the uncertain parameters to specific values. The `usubs`

command
accomplishes this, and also allows more complicated substitutions
for an element.

`usubs`

accepts a list
of element names, and respective values to substitute for them. You
can create three uncertain real parameters and use them to create
a 2-by-2 uncertain matrix `A`

.

delta = ureal('delta',2); eta = ureal('eta',6); rho = ureal('rho',-1); A = [3+delta+eta delta/eta;7+rho rho+delta*eta]

A = Uncertain matrix with 2 rows and 2 columns. The uncertainty consists of the following blocks: delta: Uncertain real, nominal = 2, variability = [-1,1], 2 occurrences eta: Uncertain real, nominal = 6, variability = [-1,1], 3 occurrences rho: Uncertain real, nominal = -1, variability = [-1,1], 1 occurrences Type "A.NominalValue" to see the nominal value, "get(A)" to see all properties, and "A.Uncertainty" to interact with the uncertain elements.

Use `usubs`

to substitute
the uncertain element named `delta`

in `A`

with
the value 2.3, leaving all other uncertain elements intact. Note that
the result, `B`

, is an uncertain matrix with dependence
only on `eta`

and `rho`

.

```
B = usubs(A,'delta',2.3)
```

B = Uncertain matrix with 2 rows and 2 columns. The uncertainty consists of the following blocks: eta: Uncertain real, nominal = 6, variability = [-1,1], 3 occurrences rho: Uncertain real, nominal = -1, variability = [-1,1], 1 occurrences Type "B.NominalValue" to see the nominal value, "get(B)" to see all properties, and "B.Uncertainty" to interact with the uncertain elements.

To set multiple elements, list individually, or group the values in a data structure. For instance, the following are the same.

B1 = usubs(A,'delta',2.3,'eta',A.Uncertainty.rho); S.delta = 2.3; S.eta = A.Uncertainty.rho; B2 = usubs(A,S);

In each case, `delta`

is replaced by 2.3, and `eta`

is
replaced by `A.Uncertainty.rho`

.

Any superfluous substitution requests are ignored. Hence, the
following returns an uncertain model that is the same as `A`

.

```
B4 = usubs(A,'fred',5);
```

An alternative syntax for `usubs`

is
to specify the substituted values in a structure, whose fieldnames
are the names of the elements being substituted with values.

Create a structure `NV`

with 2 fields, `delta`

and `eta`

.
Set the values of these fields to be the desired substituted values.
Then perform the substitution with `usubs`

.

NV.delta = 2.3; NV.eta = A.Uncertainty.rho; B6 = usubs(A,NV);

Here, `B6`

is the same as `B1`

and `B2`

above.
Again, any superfluous fields are ignored. Therefore, adding an additional
field `gamma`

to `NV`

, and substituting
does not alter the result.

NV.gamma = 0; B7 = usubs(A,NV);

Here, `B7`

is the same as `B6`

.

The commands `wcgain`

, `robuststab`

and `usample`

all return substitutable values
in this structure format. More discussion can be found in Create Arrays with usubs.

If the replacement value is the (partial and case-independent)
string `'Nominal'`

, then the listed element are replaced
with their nominal values. Therefore

```
B8 = usubs(A,fieldnames(A.Uncertainty),'nom')
```

B8 = 11.0000 0.3333 6.0000 11.0000

B9 = A.NominalValue

B9 = 11.0000 0.3333 6.0000 11.0000

are the same. It is possible to only set some of the elements
to `NominalValues`

, and would be the typical use
of `usubs`

with the `'nominal'`

argument.

Within `A`

, set `eta`

to its
nominal value, `delta`

to a random value (within
its range) and `rho`

to a specific value, say 6.5

B10 = usubs(A,'eta','nom','delta','rand','rho',6.5)

B10 = 10.5183 0.2531 13.5000 15.6100

Unfortunately, the `'nominal'`

and `'Random'`

specifiers
may not be used in the structure format. However, explicitly setting
a field of the structure to an element's nominal value, and then following
(or preceeding) the call to `usubs`

with
a call to `usample`

(to
generate the random samples) is acceptable, and achieves the same
effect.

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