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Substitute given values for uncertain elements of uncertain objects

`B = usubs(M,ElementName1,value1,ElementName2,value2,...)`

B = usubs(M,S)

B = usubs(M,...,'-once')

B = usubs(M,...,'-batch')

Use `usubs`

to substitute a specific value for an uncertain element of an
uncertain model object. The value can itself be uncertain. It needs to be the correct size, but
otherwise can be of any class, and can be an array. Hence, the result can be of any class. In
this manner, uncertain elements act as symbolic placeholders, for which specific values (which
can also contain other placeholders too) can be substituted.

`B = usubs(M,ElementName1,value1,ElementName2,value2,...)`

sets the elements in `M`

, identified by `ElementName1`

,
`ElementName2`

, etc., to the values in `value1`

,
`value2`

, etc. respectively.

You can also use the character vectors `'NominalValue'`

or
`'Random'`

as any `value`

argument. If you do so, the nominal
value or a random instance of the uncertain element is used. You can partially specify these
character vectors, instead of typing the full expression. For example, you can use
`'Nom'`

or `'Rand'`

.

`B = usubs(M,S)`

instantiates the uncertain elements of
`M`

to the values specified in the structure `S`

. The field
names of `S`

are the names of the uncertain elements to replace. The values are
the corresponding replacement values. To provide several replacement values, make
`S`

a struct array, where each struct contains one set of replacement values. A
structure such as `S`

typically comes from robustness analysis commands such as
`robstab`

, `usample`

, or `wcgain`

.

`B = usubs(M,...,'-once')`

performs vectorized substitution in the
uncertain model array `M`

. Each uncertain element is replaced by a single value,
but this value may change across the model array. To specify different substitute values for each
model in the array `M`

, use:

A cell array for each

`valueN`

that causes the uncertain element`ElementNameN`

in`M(:,:,k)`

to be replaced by`valueN(k)`

. For example, if`M`

is a 2-by-3 array, then a 2-by-3 cell array`value1`

replaces`ElementName1`

of the model`M(:,:,k)`

with the corresponding`value1(k)`

.A struct array

`S`

that specifies one set of substitute values`S(k)`

for each model`M(:,:,k)`

.

Numeric array formats are also accepted for `value1,value2,...`

. For
example, `value1`

can be a 2-by-3 array of LTI models, a numeric array of size
`[size(name1) 2 3]`

, or a 2-by-3 matrix when the uncertain element
`name1`

is scalar-valued. The array sizes of `M`

,
`S`

, `value1,value2,...`

must agree along non-singleton
dimensions. Scalar expansion takes place along singleton dimensions.

Vectorized substitution (`'-once'`

) is the default for model arrays when no
substitution method is specified.

`B = usubs(M,...,'-batch')`

performs batch substitution in the uncertain
model array `M`

. Each uncertain element is replaced by an array of values, and
the same values are used for all models in `M`

. In batch substitution,
`B`

is a model array of size `[size(M) VS]`

, where
`VS`

is the size of the array of substitute values.