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Peak gain of dynamic system frequency response

`gpeak = getPeakGain(sys)`

`gpeak = getPeakGain(sys,tol)`

`gpeak = getPeakGain(sys,tol,fband)`

```
[gpeak,fpeak]
= getPeakGain(___)
```

returns
the peak input/output gain in absolute units of the dynamic system
model, `gpeak`

= getPeakGain(`sys`

)`sys`

.

If

`sys`

is a SISO model, then the peak gain is the largest value of the frequency response magnitude.If

`sys`

is a MIMO model, then the peak gain is the largest value of the frequency response 2-norm (the largest singular value across frequency) of`sys`

. This quantity is also called the*L*norm of_{∞}`sys`

, and coincides with the*H*norm for stable systems (see_{∞}`norm`

).If

`sys`

is a model that has tunable or uncertain parameters,`getPeakGain`

evaluates the peak gain at the current or nominal value of`sys`

.If

`sys`

is a model array,`getPeakGain`

returns an array of the same size as`sys`

, where`gpeak(k) = getPeakGain(sys(:,:,k))`

.

`getPeakGain`

uses the algorithm of [1]. All eigenvalue computations are performed using structure-preserving algorithms from
the SLICOT library. For more information about the SLICOT library, see http://slicot.org.

[1] Bruisma, N.A. and M. Steinbuch, "A Fast
Algorithm to Compute the H_{∞}-Norm of
a Transfer Function Matrix," *System Control Letters*,
14 (1990), pp. 287-293.