  Identifiability and sloppiness are investigated in this paper for the
parameters of a descriptor system based on its frequency response samples. Two
metrics are suggested respectively for measuring absolute and relative
sloppiness of the parameter vector at a prescribed value. In this descriptor
system, system matrices are assumed to depend on its parameters through a
linear fractional transformation (LFT). When an associated transfer function
matrix (TFM) is of full normal row rank, a matrix rank based necessary and
sufficient condition is derived for parameter identifiability with a set of
finitely many frequency responses. This condition can be verified recursively
which is computationally quite appealing, especially when the system is of a
large scale. From this condition, an algorithm is suggested to find a set of
frequencies with which the frequency responses of the system are capable to
uniquely determine its parameters. An ellipsoid approximation is given for the
set consisting of all the parameter values with which the associated descriptor
system has a frequency response that deviates within a prescribed distance,
from that corresponding to a globally identifiable parameter vector value.
Explicit formulas are also derived for the suggested absolute and relative
sloppiness metrics.
