# SingularValuePlot

SingularValuePlot[lsys]

generates a plot of the singular values of the transfer function for the system lsys.

SingularValuePlot[lsys,{ωmin,ωmax}]

plots for the frequency range ωmin to ωmax.

SingularValuePlot[expr,{ω,ωmin,ωmax}]

plots expr using the variable ω.

# Details and Options • The system lsys can be TransferFunctionModel or StateSpaceModel, including descriptor and delay systems.
• For a system lsys with the corresponding transfer function , the following expressions are plotted:
• continuous-time system discrete-time system with sample time • SingularValuePlot treats the variable ω as local, effectively using Block.
• SingularValuePlot has the same options as Plot, with the following additions and changes:
•  SamplingPeriod None the sampling period ScalingFunctions {"Log10","dB"} the scaling functions Tolerance 0 the tolerance in computing the singular values
• The scaling functions can be specified as ScalingFunctions->{freqscale,magscale}.
• The frequency scale freqscale can be "Log10" or "Linear", which correspond to the base-10 logarithmic scale and linear scale, respectively.
• The magnitude scale magscale can be "dB" or "Absolute", which correspond to the decibel and absolute values of the magnitude, respectively.

# Examples

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## Basic Examples(3)

The singular value plot of a transfer-function model:

The transfer function can be specified as a matrix:

The singular value plot of a state-space model:

## Scope(7)

SingularValuePlot shows all the singular values:

A one-input, two-output system:

A two-input, three-output system:

A discrete-time system:

A discrete-time system specified as an expression:

Explicit frequency range:

Specify a system using its sinusoidal transfer function:

equals :

## Options(16)

### CoordinatesToolOptions(3)

Display coordinates by selecting the graphic and typing a period (.):

If the frequency is in radians/second, the corresponding values in hertz can be displayed as follows:

Display coordinates of frequency and the singular values in hertz and absolute values, respectively:

### GridLines(3)

Show grid lines:

Show only the frequency grid lines:

Show specific grid lines:

### GridLinesStyle(1)

Specify the grid line style:

### PlotLegends(4)

Use automatic legends for multiple singular values:

Use a list of text for legends:

Use LineLegend to add a overall legend label:

Place the legend above the plot:

### PlotTheme(1)

Use a theme with simple ticks and grid lines in a bright color scheme:

Change the color scheme:

### SamplingPeriod(2)

Systems specified as an expression are assumed to be in the continuous-time domain:

A discrete-time system:

### ScalingFunctions(2)

Show frequency in the linear scale:

Show the absolute values of the singular values:

## Applications(1)

A plot with frequency in rotations/minute, when the Laplace variable is in radians/second:

## Properties & Relations(1)

The singular value plot and the Bode magnitude plot are the same for SISO systems: