Worst-case disk-based stability margins of uncertain feedback loops

The worst-case disk margin is the smallest disk margin that occurs within a
specified uncertainty range. It is also the minimum guaranteed margin over the uncertainty
range. `wcdiskmargin`

estimates the worst-case disk margins and
corresponding worst-case gain and phase margins for both loop-at-a-time and multiloop
variations. The function also returns the worst-case perturbation, the combination of
uncertain elements that yields the weakest margins.

`[`

estimates the worst-case loop-at-a-time disk-based stability margins for the uncertain
negative feedback loop `wcDM`

,`wcu`

] = wcdiskmargin(`L`

,'siso')`feedback(L,eye(N))`

, where `N`

is
the number of inputs and outputs in `L`

.

While `diskmargin`

computes stability margins for a nominal model, `wcdiskmargin`

computes
the worst-case (smallest) disk margin over the modeled uncertainty in
`L`

. Disk-based margin analysis provides a stronger guarantee of robust
stability than the classical gain and phase margins. For general information about disk
margins, see Stability Analysis Using Disk Margins.

`___ = wcdiskmargin(___,`

specifies an additional eccentricity parameter that varies the shape of the disk region used
to compute the stability margins. You can use the eccentricity argument with any of the
previous syntaxes.`E`

)

`[___,`

returns a structure with additional information about the worst-case margins and the
perturbations that generate them. You can use this output argument with any of the previous
syntaxes.`info`

] = wcdiskmargin(___)

`wcdiskmargin`

assumes negative feedback. To compute the worst-case disk margins of a positive feedback system, use`wcdiskmargin(-L)`

or`wcdiskmargin(P,-C)`

.

`wcdiskmargin`

models gain (and phase) variation as
`ucomplex`

uncertainty, combines it with the specified plant uncertainty,
and uses `mussv`

to compute the worst-case disk margins and perturbation.
This generalizes the `diskmargin`

algorithm to feedback loops with
uncertainty. For more information about disk-margin computation and interpretation, see Stability Analysis Using Disk Margins.