# wcgain

Worst-case gain of uncertain system

## Syntax

## Description

`[`

calculates the worst-case
peak gain of the uncertain system `wcg`

,`wcu`

]
= wcgain(`usys`

)`usys`

. *Peak
gain* refers to the maximum gain over frequency (*H*_{∞} norm).
For multi-input, multi-output (MIMO) systems, gain refers to the largest
singular value of the frequency response matrix. (See `sigma`

for more information about singular
values.) The structure `wcg`

contains upper and
lower bounds on the worst-case gain and the critical frequency at
which the lower bound peaks. (See Worst-Case Gain.) The structure `wcu`

contains
the values of the uncertain elements of `usys`

that
cause the worst-case peak gain.

`[`

restricts
worst-case computation to the frequencies specified by `wcg`

,`wcu`

]
= wcgain(`usys`

,`w`

)`w`

.

If

`w`

is a cell array of the form`{wmin,wmax}`

, then`wcgain`

returns the worst-case gain in the interval between`wmin`

and`wmax`

.If

`w`

is a vector of frequencies, then`wcgain`

calculates the worst-case gain at the specified frequencies only, and returns the worst of those gains.

## Examples

## Input Arguments

## Output Arguments

## More About

## Algorithms

Computing the worst-case gain at a particular frequency is equivalent
to computing the structured singular value, *μ*,
for some appropriate block structure (*μ*-analysis).

For `uss`

and `genss`

models, `wcgain(usys)`

and `wcgain(usys,{wmin,wmax})`

use
an algorithm that finds the worst-case gain across frequency. This
algorithm does not rely on frequency gridding and is not adversely
affected by sharp peaks of the *μ* structured
singular value. See Getting Reliable Estimates of Robustness Margins for
more information.

For `ufrd`

and `genfrd`

models, `wcgain`

computes
the *μ* lower and upper bounds at each frequency
point. This computation offers no guarantee between frequency points
and can be inaccurate if the uncertainty gives rise to sharp resonances.
The syntax `wcgain(uss,w)`

, where `w`

is
a vector of frequency points, is the same as `wcgain(ufrd(uss,w))`

and
also relies on frequency gridding to compute the worst-case gain.

In general, the algorithm for state-space models is faster and
safer than the frequency-gridding approach. In some cases, however,
the state-space algorithm requires many *μ* calculations.
In those cases, specifying a frequency grid as a vector `w`

can
be faster, provided that the worst-case gain varies smoothly with
frequency. Such smooth variation is typical for systems with dynamic
uncertainty.

## Version History

**Introduced before R2006a**