# sigma

Singular values of frequency response of dynamic system

## Description

`[`

returns the singular values
`sv`

,`wout`

]
= sigma(`sys`

)`sv`

of the frequency response of dynamic system model
`sys`

at each frequency in the vector `wout`

. The
function automatically determines frequencies to plot based on system dynamics.

`sigma(___)`

plots the singular values of the frequency
response of `sys`

with default plotting options for all of the previous
input argument combinations. If `sys`

is a single-input, single-output
(SISO) model, then the singular value plot is similar to its Bode magnitude response. For
more plot customization options, use `sigmaplot`

.

To plot singular values for multiple dynamic systems on the same plot, you can specify

`sys`

as a comma-separated list of models. For example,`sigma(sys1,sys2,sys3)`

plots the singular values for three models on the same plot.To specify a color, line style, and marker for each system in the plot, specify a

`LineSpec`

value for each system. For example,`sigma(sys1,LineSpec1,sys2,LineSpec2)`

plots two models and specifies their plot style. For more information on specifying a`LineSpec`

value, see`sigmaplot`

.

## Examples

## Input Arguments

## Output Arguments

## Algorithms

`sigma`

uses the MATLAB^{®} function `svd`

to compute the singular values of the complex
frequency response.

For an

`frd`

model,`sigma`

computes the singular values of`sys.ResponseData`

at the frequencies,`sys.Frequency`

.For continuous-time

`tf`

,`ss`

, or`zpk`

models with transfer function*H*(*s*),`sigma`

computes the singular values of*H*(*j**ω*) as a function of the frequency*ω*.For discrete-time

`tf`

,`ss`

, or`zpk`

models with transfer function*H*(*z*) and sample time*T*,_{s}`sigma`

computes the singular values of$$H\left({e}^{j\omega {T}_{s}}\right)$$

for frequencies

*ω*between 0 and the Nyquist frequency*ω*= π/_{N}*T*._{s}

## Version History

**Introduced before R2006a**