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Create uncertain linear time-invariant object

H = ultidyn('Name',iosize) H = ultidyn('Name',iosize,'Property1',Value1,'Property2',Value2,...)

`H = ultidyn('Name',iosize)`

creates an uncertain linear, time-invariant objects are used to represent unknown dynamic objects whose only known attributes are bounds on their frequency response. Uncertain linear, time-invariant objects have a name (the `Name`

property), and an input/output size (`ioSize`

property).

Trailing Property/Value pairs are allowed in the construction.

`H = ultidyn('name',iosize,'Property1',Value1,'Property2',Value2,...)`

The property `Type`

is `'GainBounded'`

(default) or `'PositiveReal'`

, and describes in what form the knowledge about the object's frequency response is specified.

If

`Type`

is`'GainBounded'`

, then the knowledge is an upper bound on the magnitude (i.e., absolute value), namely`abs(H)<= Bound`

at all frequencies. The matrix generalization of this is ∥`H`

∥`<= Bound`

.If

`Type`

is`'PositiveReal'`

then the knowledge is a lower bound on the real part, namely`Real(H) >= Bound`

at all frequencies. The matrix generalization of this is`H+H' >= 2*Bound`

The property `Bound`

is a real, scalar that quantifies the bound on the frequency response of the uncertain object as described above.

The property `SampleStateDimension`

is a positive integer, defining the state
dimension of random samples of the uncertain object when sampled with
`usample`

. The default value is 3.

The property `AutoSimplify`

controls how expressions involving the uncertain matrix are simplified. Its default value is` 'basic'`

, which means elementary methods of simplification are applied as operations are completed. Other values for `AutoSimplify`

are` 'off'`

, no simplification performed, and` 'full'`

which applies model-reduction-like techniques to the uncertain object.

Use the property `SampleMaxFrequency`

to limit the natural frequency for sampling. Randomly sampled uncertain dynamics are no faster than the specified value. The default value is `Inf`

(no limit).

To model frequency-dependent uncertainty levels, multiply the `ultidyn`

object by a suitable shaping filter. For example, for a `ultidyn`

object `dH`

, the following commands specify an uncertainty bound that increases from 0.1 at low frequencies to 10 at high frequencies.

W = tf([1 .1],[.1 1]); dH = W*dH;