Uncertain linear, time-invariant objects,
ultidyn, are used to represent unknown
linear, time-invariant dynamic objects, whose only known attributes
are bounds on their frequency response. Uncertain linear, time-invariant
objects have an internal name (the
and are created by specifying their size (number of outputs and number
Type specifies whether the known
attributes about the frequency response are related to gain or phase.
Type may be
The default value is
Bound is a single number, which
Type, completely specifies what is known
about the uncertain frequency response. Specifically, if Δ is
ultidyn element, and if
γ denotes the value of the
then the element represents the set of all stable, linear, time-invariant
systems whose frequency response satisfies certain conditions:
all frequencies. When
the default value for
Bound (i.e., γ)
is 1. The
NominalValue of Δ is always the
'PositiveReal', Δ(ω) + Δ*(ω) ≥ 2γ·
for all frequencies. When
the default value for
Bound (i.e., γ) is
NominalValue is always (γ + 1 +2|γ|)I.
All properties of a
can be accessed with
NominalValue is determined from
and not accessible with
set). The properties are
Nominal value of element
Norm bound or minimum real
State-space dimension of random samples of this uncertain element
SampleStateDim property specifies the
state dimension of random samples of the element when using
usample. The default value is 1. The
serves the same function as in the uncertain real parameter.
You can create a 2-by-3 gain-bounded 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
is interpreted as a continuous-time, system with uncertain behavior,
quantified by bounds (gain or real-part) on its frequency response.
To see this, create a
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
is an uncertain element of an uncertain state space model (
uss), then the time-domain characteristic
of the element is determined from the time-domain characteristic of
the system. The bounds (gain-bounded or positivity) apply to the frequency-response
of the element. This is explained and demonstrated in Interpreting Uncertainty in Discrete Time.