Uncertain linear, timeinvariant objects, ultidyn
, are used to represent unknown
linear, timeinvariant dynamic objects, whose only known attributes
are bounds on their frequency response. Uncertain linear, timeinvariant
objects have an internal name (the Name
property),
and are created by specifying their size (number of outputs and number
of inputs).
The property Type
specifies whether the known
attributes about the frequency response are related to gain or phase.
The property Type
may be 'GainBounded'
or 'PositiveReal'
.
The default value is 'GainBounded'
.
The property Bound
is a single number, which
along with Type
, completely specifies what is known
about the uncertain frequency response. Specifically, if Δ is
an ultidyn
element, and if
γ denotes the value of the Bound
property,
then the element represents the set of all stable, linear, timeinvariant
systems whose frequency response satisfies certain conditions:
If Type
is 'GainBounded'
, $$\dot{\overline{\sigma}}\left[\Delta \left(\omega \right)\right]\le \gamma $$ for
all frequencies. When Type
is 'GainBounded'
,
the default value for Bound
(i.e., γ)
is 1. The NominalValue
of Δ is always the
0matrix.
If Type
is 'PositiveReal'
, Δ(ω) + Δ^{*}(ω) ≥ 2γ·
for all frequencies. When Type
is 'PositiveReal'
,
the default value for Bound
(i.e., γ) is
0. The NominalValue
is always (γ + 1 +2γ)I.
All properties of a ultidyn
are
can be accessed with get
and set
(although
the NominalValue
is determined from Type
and Bound
,
and not accessible with set
). The properties are
Properties  Meaning  Class 

 Internal Name 

 Nominal value of element 




 Norm bound or minimum real 

 Statespace dimension of random samples of this uncertain element 




The SampleStateDim
property specifies the
state dimension of random samples of the element when using usample
. The default value is 1. The AutoSimplify
property
serves the same function as in the uncertain real parameter.
You can create a 2by3 gainbounded uncertain linear dynamics element. Verify its size, and check the properties.
f = ultidyn('f',[2 3]); size(f) ans = 2 3 get(f) Name: 'f' NominalValue: [2x3 double] Type: 'GainBounded' Bound: 1 SampleStateDim: 1 AutoSimplify: 'basic'
On its own, every ultidyn
element
is interpreted as a continuoustime, system with uncertain behavior,
quantified by bounds (gain or realpart) on its frequency response.
To see this, create a ultidyn
,
and view the sample time of several random samples of the element.
h = ultidyn('h',[1 1]); get(usample(h),'Ts') ans = 0 get(usample(h),'Ts') ans = 0 get(usample(h),'Ts') ans = 0
However, when a ultidyn
element
is an uncertain element of an uncertain state space model (uss
), then the timedomain characteristic
of the element is determined from the timedomain characteristic of
the system. The bounds (gainbounded or positivity) apply to the frequencyresponse
of the element. This is explained and demonstrated in Interpreting Uncertainty in Discrete Time.