2.2. MODELING UNCERTAINSYSTEMS 21
Figure 2.6: Example model: multiplicative output p erturbation with weighted output
noise
References to a robust control model will imply a description of the form given in
Equation 2.8.
As a example, consider one of the most common perturbation model descriptions,
illustrated in Figure 2.6. This model represents a perturbed system with bounded noise
at the output.
The example model is given by,
y=Wnw+(I+∆W
u
)P
nomu.
The system Wnis a frequency dependent weight on the noise signal, w. This allows us
to use a normalized representationfor w. In other words the model includes the
assumption that kwk∞≤1. Similarly, we assumethat k∆k∞≤1andW
uis a frequency
dependent weight which specifies the contribution of the perturbation at each frequency.
In a typical model Wnwill be small (assuming that the noise is small compared to the
nominal output) and Wuwill increase at high frequencies (to capture the likely case that
we know less about the model at higher frequencies). The LFT representation of this
model is,
y=Fu(P,∆) hw
ui,
where
P="00W
u
P
nom
IW
nP
nom #