# norm

Norm of linear model

## Syntax

## Description

or
`n`

= norm(`sys`

)

returns the root-mean-squares of the impulse response of the linear dynamic
system model `n`

=
norm(`sys`

,2)`sys`

. This value is equivalent to the *H*_{2} norm of
`sys`

.

returns the `n`

= norm(`sys`

,Inf)*L _{∞}* norm (Control System Toolbox) of

`sys`

, which is the peak gain of the frequency response
of `sys`

across frequencies. For MIMO systems, this quantity
is the peak gain over all frequencies and all input directions, which
corresponds to the peak value of the largest singular value of
`sys`

. For stable systems, the
*L*norm is equivalent to the

_{∞}*H*

_{∞}norm. For more information, see

`hinfnorm`

(Robust Control Toolbox). ## Examples

## Input Arguments

## Output Arguments

## More About

## Algorithms

After converting `sys`

to a state space model,
`norm`

uses the same algorithm as `covar`

(Control System Toolbox) for the *H*_{2} norm. For the
*L*_{∞} norm, `norm`

uses the algorithm of [1]. `norm`

computes the peak gain using 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 before R2006a**

## See Also

`freqresp`

| `sigma`

(Control System Toolbox) | `getPeakGain`

(Control System Toolbox) | `hinfnorm`

(Robust Control Toolbox)