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


plots for the frequency range ωmin to 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 Nonethe sampling period
    ScalingFunctions {"Log10","dB"}the scaling functions
    Tolerance0the 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.


open allclose all

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:

Generalizations & Extensions  (1)

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:

Wolfram Research (2010), SingularValuePlot, Wolfram Language function, (updated 2014).


Wolfram Research (2010), SingularValuePlot, Wolfram Language function, (updated 2014).


Wolfram Language. 2010. "SingularValuePlot." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014.


Wolfram Language. (2010). SingularValuePlot. Wolfram Language & System Documentation Center. Retrieved from


@misc{reference.wolfram_2022_singularvalueplot, author="Wolfram Research", title="{SingularValuePlot}", year="2014", howpublished="\url{}", note=[Accessed: 06-June-2023 ]}


@online{reference.wolfram_2022_singularvalueplot, organization={Wolfram Research}, title={SingularValuePlot}, year={2014}, url={}, note=[Accessed: 06-June-2023 ]}