Implement uncertainty measure computation

[timeverettadams]

Motivation

There is no standard method for comparing the "size" of unstructured LTI norm-bounded uncertainty sets. Current methods include evaluating the maximum singular values of the uncertainty weights W_L and W_R across frequencies. This only evaluates the worst-case perturbations of the uncertainty set. Moreover, the uncertainty weights represent different metrics (absolute deviation, relative deviation, etc.) across uncertainty models, so the comparison of these weights across uncertainty models is not meaningful.

A more appropriate metric for the size of the uncertainty set is the Lebesgue measure (generalized notion of volume) of the set of off-nominal models for the equivalent additive uncertainty model.

Proposed Changes

Main Changes

• Implementation of uncertainty measure computation.
  • Computation of equivalent additive uncertainty model.
  • Computation of minimal additive uncertainty model representation.
  • Computation of additive uncertainty measure.

Additional Changes

• Computation of optimal weights for full uncertainty weights.
• Vectorization of uncertainty residual computation across frequencies.
• Update uncertainty weight fit interface for different uncertainty weight structures.
• Update uncertainty weight fit plots.