# getPeakGain

Peak gain of dynamic system frequency response

## Syntax

## Description

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))`

.

## Examples

## Input Arguments

## Output Arguments

## Algorithms

`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 https://github.com/SLICOT.

## References

[1] Bruinsma, N.A., and M. Steinbuch. "A Fast Algorithm to Compute the
H_{∞} Norm of a Transfer Function Matrix."
*Systems & Control Letters*, 14, no.4 (April 1990):
287–93.

## Version History

**Introduced in R2012a**