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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
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Generalizations & Extensions  
Options  
AspectRatio  
Axes  
AxesLabel  
Show More Show More
AxesOrigin  
AxesStyle  
CoordinatesToolOptions  
GridLines  
GridLinesStyle  
ImageSize  
PlotLegends  
PlotTheme  
SamplingPeriod  
ScalingFunctions  
Ticks  
TicksStyle  
Applications  
Properties & Relations  
See Also
Related Guides
History
Cite this Page

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

Examples

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Basic Examples  (3)

The singular value plot of a transfer-function model:

Wolfram Language code: SingularValuePlot[TransferFunctionModel[{{{-100 + s, 10*(1 + s)}, {-10*(1 + s), -100 + s}}, 100 + s^2}, s]]

The transfer function can be specified as a matrix:

Wolfram Language code: SingularValuePlot[TransferFunctionModel[{{{87.8, -86.4}, {108.2, -109.6}}, 1 + 75*s}, s], {(1/10^4), 10^2}]

The singular value plot of a state-space model:

Wolfram Language code: SingularValuePlot[StateSpaceModel[{{{-0.01, 0}, {0, -0.02}}, {{1, 1}, {-0.004, 0.002}}, {{0.01, 0}, {0, 1}}, {{0, 0}, {0, 0}}}, SamplingPeriod -> None, SystemsModelLabels -> None], {0.001, 1}]

Scope  (7)

SingularValuePlot shows all the singular values:

Wolfram Language code: SingularValuePlot[TransferFunctionModel[{{{2*s, 1, 1}, {2, -1 + s, s}, {1, 2, s}}, {{0.7 + s^2, 4 + s, s}, {1 + s, 2 + s, 5 + s^2}, {3 + s, 4 + s, 1}}}, s]]

A one-input, two-output system:

Wolfram Language code: SingularValuePlot[TransferFunctionModel[{{{1}, {1}}, {{s}, {1 + s}}}, s]]

A two-input, three-output system:

Wolfram Language code: SingularValuePlot[TransferFunctionModel[{{{1 + s, s}, {1 + s, 3*s}, {1, s^2}}, {{1 + s^2, 4 + s + s^2}, {1 + s^2, 5 + s}, {s, 3 + 2*s + s^2}}}, s]]

A discrete-time system:

Wolfram Language code: SingularValuePlot[TransferFunctionModel[{{{1.7182, 3.1945}, {2, 0.4323}}, {{-2.7182 + z, -7.389 + z}, {-1 + z, -0.1353 + z}}}, z, SamplingPeriod -> 1]]

A discrete-time system specified as an expression:

Wolfram Language code: SingularValuePlot[TransferFunctionModel[{{{0.6321, 4.9027*(0.2356 + z)}, {31.9452, 1.5836}}, {{-0.3678 + z, (-7.389 + z)*(-0.3678 + z)}, {-7.389 + z, -0.04978 + z}}}, z, SamplingPeriod -> 1]]

Explicit frequency range:

Wolfram Language code: SingularValuePlot[TransferFunctionModel[{{{1 + s, 2}, {1, 0.2*(10 + s)}}, {{5 + 0.2*s + s^2, 3 + s}, {s, 50 + s}}}, s], {0.1, 500}]

Specify a system using its sinusoidal transfer function:

Wolfram Language code: SingularValuePlot[(10/1 - 5 I w - I w^3)(| | | | | ------ | --- | ---------------- | | -w^2 | I w | 1 | | 0 | 0 | 10 + 5 I w - w^2 | | 10 I w | 0 | 1 |), w]

Specify an explicit frequency range:

Wolfram Language code: SingularValuePlot[(10/1 - 5 I w - I w^3)(| | | | | ------ | --- | ---------------- | | -w^2 | I w | 1 | | 0 | 0 | 10 + 5 I w - w^2 | | 10 I w | 0 | 1 |), {w, 10^-3, 10^3}]

Generalizations & Extensions  (1)

A singular value plot can be obtained from a transfer-function model or directly from its expression:

Wolfram Language code: g = {{(10 (1 + s)/100 + 0.2 s + s^2), (1/1 + s)}, {(2.5  + s/10 + 2 s + s^2), (5 (1 + s)/6 + 5 s + s^2)}};
Wolfram Language code: {SingularValuePlot[TransferFunctionModel[g, s]], SingularValuePlot[g]}

Options  (46)

AspectRatio  (3)

By default, SingularValuePlot uses a fixed height-to-width ratio for the plot:

Wolfram Language code: SingularValuePlot[TransferFunctionModel[{{{-100 + s, 10 (1 + s)}, {-10 (1 + s), -100 + s}}, 100 + s^2}, s]]

Make the height the same as the width with AspectRatio1:

Wolfram Language code: SingularValuePlot[TransferFunctionModel[{{{-100 + s, 10 (1 + s)}, {-10 (1 + s), -100 + s}}, 100 + s^2}, s], AspectRatio -> 1]

AspectRatioFull adjusts the height and width to tightly fit inside other constructs:

Wolfram Language code: plot = SingularValuePlot[TransferFunctionModel[{{{-100 + s, 10 (1 + s)}, {-10 (1 + s), -100 + s}}, 100 + s^2}, s], AspectRatio -> Full];
Wolfram Language code: {Framed[Pane[plot, {75, 100}]], Framed[Pane[plot, {100, 100}]], Framed[Pane[plot, {100, 50}]]}

Axes  (3)

By default, Axes are drawn:

Wolfram Language code: SingularValuePlot[TransferFunctionModel[{{{-100 + s, 10 (1 + s)}, {-10 (1 + s), -100 + s}}, 100 + s^2}, s]]

Use AxesFalse to turn off axes:

Wolfram Language code: SingularValuePlot[TransferFunctionModel[{{{-100 + s, 10 (1 + s)}, {-10 (1 + s), -100 + s}}, 100 + s^2}, s], Axes -> False]

Turn on each axis individually:

Wolfram Language code: {SingularValuePlot[TransferFunctionModel[{{{-100 + s, 10 (1 + s)}, {-10 (1 + s), -100 + s}}, 100 + s^2}, s], Axes -> {True, False}], SingularValuePlot[TransferFunctionModel[{{{-100 + s, 10 (1 + s)}, {-10 (1 + s), -100 + s}}, 100 + s^2}, s], Axes -> {False, True}]}

AxesLabel  (3)

No axes labels are drawn by default:

Wolfram Language code: SingularValuePlot[TransferFunctionModel[{{{-100 + s, 10 (1 + s)}, {-10 (1 + s), -100 + s}}, 100 + s^2}, s]]

Place a label on the axis:

Wolfram Language code: SingularValuePlot[TransferFunctionModel[{{{-100 + s, 10 (1 + s)}, {-10 (1 + s), -100 + s}}, 100 + s^2}, s], AxesLabel -> label]

Specify axes labels:

Wolfram Language code: SingularValuePlot[TransferFunctionModel[{{{-100 + s, 10 (1 + s)}, {-10 (1 + s), -100 + s}}, 100 + s^2}, s], AxesLabel -> {label1, label2}]

AxesOrigin  (2)

The position of the axes is determined automatically:

Wolfram Language code: SingularValuePlot[TransferFunctionModel[{{{-100 + s, 10 (1 + s)}, {-10 (1 + s), -100 + s}}, 100 + s^2}, s]]

Specify an explicit origin for the axes:

Wolfram Language code: SingularValuePlot[TransferFunctionModel[{{{-100 + s, 10 (1 + s)}, {-10 (1 + s), -100 + s}}, 100 + s^2}, s], AxesOrigin -> {20, 10}]

AxesStyle  (4)

Change the style for the axes:

Wolfram Language code: SingularValuePlot[TransferFunctionModel[{{{-100 + s, 10 (1 + s)}, {-10 (1 + s), -100 + s}}, 100 + s^2}, s], AxesStyle -> Red]

Specify the style of each axis:

Wolfram Language code: SingularValuePlot[TransferFunctionModel[{{{-100 + s, 10 (1 + s)}, {-10 (1 + s), -100 + s}}, 100 + s^2}, s], AxesStyle -> {{Thick, Red}, {Thick, Blue}}]

Use different styles for the ticks and the axes:

Wolfram Language code: SingularValuePlot[TransferFunctionModel[{{{-100 + s, 10 (1 + s)}, {-10 (1 + s), -100 + s}}, 100 + s^2}, s], AxesStyle -> Green, TicksStyle -> Red]

Use different styles for the labels and the axes:

Wolfram Language code: SingularValuePlot[TransferFunctionModel[{{{-100 + s, 10 (1 + s)}, {-10 (1 + s), -100 + s}}, 100 + s^2}, s], AxesStyle -> Green, LabelStyle -> Red]

CoordinatesToolOptions  (3)

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

Wolfram Language code: SingularValuePlot[TransferFunctionModel[{{{2*s, 2*s, 2*s}, {2, 2, s}}, {{10 + s, 5 + s, 1 + s}, {1 + s, 3 + s, 6 + s}}}, s]]

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

Wolfram Language code: tfm = TransferFunctionModel[{{{2*s, 2*s, 2*s}, {2, 2, s}}, {{10 + s, 5 + s, 1 + s}, {1 + s, 3 + s, 6 + s}}}, s];
Wolfram Language code: SingularValuePlot[tfm, CoordinatesToolOptions -> ("DisplayFunction" -> Function[pt, {(pt[[1]]/2 π), pt[[2]]}])]

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

Wolfram Language code: tfm = TransferFunctionModel[{{{2*s, 2*s, 2*s}, {2, 2, s}}, {{10 + s, 5 + s, 1 + s}, {1 + s, 3 + s, 6 + s}}}, s];
Wolfram Language code: SingularValuePlot[tfm, CoordinatesToolOptions -> ("DisplayFunction" -> Function[pt, {(pt[[1]]/2 π), 10^(pt[[2]]/20)}])]

GridLines  (3)

Show grid lines:

Wolfram Language code: tfm = TransferFunctionModel[{{{15 + 10*s, 2}, {5, 2}}, {{1 + 5*s + s^2, 2 + 3*s + s^3}, {1 + 4*s + s^2, 1 + s}}}, s];
Wolfram Language code: SingularValuePlot[tfm, GridLines -> Automatic]

Show only the frequency grid lines:

Wolfram Language code: tfm = TransferFunctionModel[{{{15 + 10*s, 2}, {5, 2}}, {{1 + 5*s + s^2, 2 + 3*s + s^3}, {1 + 4*s + s^2, 1 + s}}}, s];
Wolfram Language code: SingularValuePlot[tfm, GridLines -> {Automatic, None}]

Show specific grid lines:

Wolfram Language code: tfm = TransferFunctionModel[{{{15 + 10*s, 2}, {5, 2}}, {{1 + 5*s + s^2, 2 + 3*s + s^3}, {1 + 4*s + s^2, 1 + s}}}, s];
Wolfram Language code: SingularValuePlot[tfm, GridLines -> {NestList[10 #&, 0.01, 3], Range[-30, 30, 10]}]

GridLinesStyle  (1)

Specify the grid line style:

Wolfram Language code: tfm = TransferFunctionModel[{{{1, 3.2}, {1, 2.1}}, {{1.4 + s, 6 + s}, {-1 + s, 1.4 + s}}}, s];
Wolfram Language code: SingularValuePlot[tfm, GridLines -> Automatic, GridLinesStyle -> {LightRed, LightBlue}]

ImageSize  (7)

Use named sizes such as Tiny, Small, Medium and Large:

Wolfram Language code: {SingularValuePlot[TransferFunctionModel[{{{-100 + s, 10 (1 + s)}, {-10 (1 + s), -100 + s}}, 100 + s^2}, s], ImageSize -> Tiny], SingularValuePlot[TransferFunctionModel[{{{-100 + s, 10 (1 + s)}, {-10 (1 + s), -100 + s}}, 100 + s^2}, s], ImageSize -> Small]}

Specify the width of the plot:

Wolfram Language code: {SingularValuePlot[TransferFunctionModel[{{{-100 + s, 10 (1 + s)}, {-10 (1 + s), -100 + s}}, 100 + s^2}, s], ImageSize -> 150], SingularValuePlot[TransferFunctionModel[{{{-100 + s, 10 (1 + s)}, {-10 (1 + s), -100 + s}}, 100 + s^2}, s], AspectRatio -> 1.5, ImageSize -> 150]}

Specify the height of the plot:

Wolfram Language code: {SingularValuePlot[TransferFunctionModel[{{{-100 + s, 10 (1 + s)}, {-10 (1 + s), -100 + s}}, 100 + s^2}, s], ImageSize -> {Automatic, 150}], SingularValuePlot[TransferFunctionModel[{{{-100 + s, 10 (1 + s)}, {-10 (1 + s), -100 + s}}, 100 + s^2}, s], AspectRatio -> 2, ImageSize -> {Automatic, 150}]}

Allow the width and height to be up to a certain size:

Wolfram Language code: {SingularValuePlot[TransferFunctionModel[{{{-100 + s, 10 (1 + s)}, {-10 (1 + s), -100 + s}}, 100 + s^2}, s], ImageSize -> UpTo[200]], SingularValuePlot[TransferFunctionModel[{{{-100 + s, 10 (1 + s)}, {-10 (1 + s), -100 + s}}, 100 + s^2}, s], AspectRatio -> 2, ImageSize -> UpTo[200]]}

Specify the width and height for a graphic, padding with space if necessary:

Wolfram Language code: SingularValuePlot[TransferFunctionModel[{{{-100 + s, 10 (1 + s)}, {-10 (1 + s), -100 + s}}, 100 + s^2}, s], ImageSize -> {200, 200}, Background -> StandardGray]

Setting AspectRatioFull will fill the available space:

Wolfram Language code: SingularValuePlot[TransferFunctionModel[{{{-100 + s, 10 (1 + s)}, {-10 (1 + s), -100 + s}}, 100 + s^2}, s], AspectRatio -> Full, ImageSize -> {200, 200}, Background -> StandardGray]

Use maximum sizes for the width and height:

Wolfram Language code: {SingularValuePlot[TransferFunctionModel[{{{-100 + s, 10 (1 + s)}, {-10 (1 + s), -100 + s}}, 100 + s^2}, s], ImageSize -> {UpTo[150], UpTo[100]}], SingularValuePlot[TransferFunctionModel[{{{-100 + s, 10 (1 + s)}, {-10 (1 + s), -100 + s}}, 100 + s^2}, s], AspectRatio -> 2, ImageSize -> {UpTo[150], UpTo[100]}]}

Use ImageSizeFull to fill the available space in an object:

Wolfram Language code: Framed[Pane[SingularValuePlot[TransferFunctionModel[{{{-100 + s, 10 (1 + s)}, {-10 (1 + s), -100 + s}}, 100 + s^2}, s], ImageSize -> Full, Background -> StandardGray], {200, 100}]]

Specify the image size as a fraction of the available space:

Wolfram Language code: Framed[Pane[SingularValuePlot[TransferFunctionModel[{{{-100 + s, 10 (1 + s)}, {-10 (1 + s), -100 + s}}, 100 + s^2}, s], AspectRatio -> Full, ImageSize -> {Scaled[0.5], Scaled[0.5]}, Background -> StandardGray], {200, 200}]]

PlotLegends  (4)

Use automatic legends for multiple singular values:

Wolfram Language code: SingularValuePlot[TransferFunctionModel[{{{1, 3.2}, {1, 2.1}}, {{1.4 + s, 6 + s}, {-1 + s, 1.4 + s}}}, s], PlotLegends -> Automatic]

Use a list of text for legends:

Wolfram Language code: SingularValuePlot[TransferFunctionModel[{{{2*s, 1, 1}, {2, -1 + s, s}, {1, 2, s}}, {{0.7 + s^2, 4 + s, s}, {1 + s, 2 + s, 5 + s^2}, {3 + s, 4 + s, 1}}}, s], PlotLegends -> {"one", "two", "three"}]

Use LineLegend to add a overall legend label:

Wolfram Language code: SingularValuePlot[TransferFunctionModel[{{{2*s, 1, 1}, {2, -1 + s, s}, {1, 2, s}}, {{0.7 + s^2, 4 + s, s}, {1 + s, 2 + s, 5 + s^2}, {3 + s, 4 + s, 1}}}, s], PlotLegends -> LineLegend[{"one", "two", "three"}, LegendLabel -> "σ"]]

Place the legend above the plot:

Wolfram Language code: SingularValuePlot[TransferFunctionModel[{{{2*s, 1, 1}, {2, -1 + s, s}, {1, 2, s}}, {{0.7 + s^2, 4 + s, s}, {1 + s, 2 + s, 5 + s^2}, {3 + s, 4 + s, 1}}}, s], PlotLegends -> Placed[LineLegend[{"one", "two", "three"}, LegendLabel -> "σ"], Above]]

PlotTheme  (1)

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

Wolfram Language code: tfm = TransferFunctionModel[{{{15 + 10*s, 2}, {5, 2}}, {{1 + 5*s + s^2, 2 + 3*s + s^3}, {1 + 4*s + s^2, 1 + s}}}, s]
Wolfram Language code: SingularValuePlot[tfm, PlotTheme -> "Business"]

Change the color scheme:

Wolfram Language code: SingularValuePlot[tfm, PlotTheme -> "Business", PlotStyle -> 96]

SamplingPeriod  (2)

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

Wolfram Language code: SingularValuePlot[TransferFunctionModel[{{{10, 5}, {1, 5}}, {{10 + s, 5 + s}, {s, 1}}}, s]]

A discrete-time system:

Wolfram Language code: SingularValuePlot[TransferFunctionModel[{{{z, 0.5 - 1.5*z + z^2}, {-0.4 + z, 2}}, {{-1 + z, 0.5 - z + z^2}, {-0.6 + z, -1 + z}}}, z, SamplingPeriod -> 1]]

ScalingFunctions  (2)

Show frequency in the linear scale:

Wolfram Language code: tfm = TransferFunctionModel[{{{3, (-1 + s)*(2 + s)}, {1, 1}}, {{1 + s, (1 + s)*(3 + s)}, {1 + s, (1 + s)*(3 + s)}}}, s]
Wolfram Language code: SingularValuePlot[tfm, ScalingFunctions -> {"Linear", Automatic}]

Show the absolute values of the singular values:

Wolfram Language code: tfm = TransferFunctionModel[{{{3, (-1 + s)*(2 + s)}, {1, 1}}, {{1 + s, (1 + s)*(3 + s)}, {1 + s, (1 + s)*(3 + s)}}}, s]
Wolfram Language code: SingularValuePlot[tfm, ScalingFunctions -> {Automatic, "Absolute"}]

Ticks  (4)

Ticks are placed automatically in each plot:

Wolfram Language code: SingularValuePlot[TransferFunctionModel[{{{-100 + s, 10*(1 + s)}, {-10*(1 + s), -100 + s}}, 100 + s^2}, s]]

Use TicksNone to not draw any tick marks:

Wolfram Language code: SingularValuePlot[TransferFunctionModel[{{{-100 + s, 10*(1 + s)}, {-10*(1 + s), -100 + s}}, 100 + s^2}, s], Ticks -> None]

Place tick marks at specific positions:

Wolfram Language code: SingularValuePlot[TransferFunctionModel[{{{-100 + s, 10*(1 + s)}, {-10*(1 + s), -100 + s}}, 100 + s^2}, s], Ticks -> {{.1, 10, 900}, {-30, 0, 30}}]

Draw tick marks at the specified positions with the specified labels:

Wolfram Language code: SingularValuePlot[TransferFunctionModel[{{{-100 + s, 10*(1 + s)}, {-10*(1 + s), -100 + s}}, 100 + s^2}, s], Ticks -> {{{.1, a}, {10, b}, {900, c}}, {{-30, -d}, {0, 0}, {30, d}}}]

TicksStyle  (4)

Specify the overall tick style, including the tick labels:

Wolfram Language code: SingularValuePlot[TransferFunctionModel[{{{-100 + s, 10*(1 + s)}, {-10*(1 + s), -100 + s}}, 100 + s^2}, s], TicksStyle -> Directive[Blue, Thick]]

Specify the overall tick style for each of the axes:

Wolfram Language code: SingularValuePlot[TransferFunctionModel[{{{-100 + s, 10*(1 + s)}, {-10*(1 + s), -100 + s}}, 100 + s^2}, s], TicksStyle -> {Directive[Blue, Thick], Directive[Red, Thick]}]

Specify tick marks with scaled lengths:

Wolfram Language code: SingularValuePlot[TransferFunctionModel[{{{-100 + s, 10*(1 + s)}, {-10*(1 + s), -100 + s}}, 100 + s^2}, s], Ticks -> {{{.1, a, .3}, {10, b, .26}, {900, c, .05}}, {{-30, -d, .79}, {0, 0, Automatic}, {30, d, .48}}}]

Customize each tick with position, length, labeling and styling:

Wolfram Language code: SingularValuePlot[TransferFunctionModel[{{{-100 + s, 10*(1 + s)}, {-10*(1 + s), -100 + s}}, 100 + s^2}, s], Ticks -> {{{.1, a, .3, Directive[Red, Thick, Dashed]}, {10, b, .26, Directive[Red, Dashed]}, {900, c, .05, Directive[Red, Thick]}}, {{-30, -d, .79, Directive[Blue, Thick, Dashed]}, {0, 0, Automatic, Directive[Blue, Thick]}, {30, d, .48, Directive[Blue, Dashed]}}}]

Applications  (1)

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

Wolfram Language code: tfm = TransferFunctionModel[{{{1, s}, {s^2, 3}}, 5 - s + s^2}, s];
Wolfram Language code: SingularValuePlot[tfm[I (2 π/60) f], f]

Properties & Relations  (1)

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

Wolfram Language code: tfm = TransferFunctionModel[{{{1 + s}}, 1 + s + s^2}, s];
Wolfram Language code: {SingularValuePlot[tfm], BodePlot[tfm, PlotLayout -> "Magnitude", Frame -> False]}
Wolfram Research (2010), SingularValuePlot, Wolfram Language function, https://reference.wolfram.com/language/ref/SingularValuePlot.html (updated 2014).

Text

Wolfram Research (2010), SingularValuePlot, Wolfram Language function, https://reference.wolfram.com/language/ref/SingularValuePlot.html (updated 2014).

CMS

Wolfram Language. 2010. "SingularValuePlot." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014. https://reference.wolfram.com/language/ref/SingularValuePlot.html.

APA

Wolfram Language. (2010). SingularValuePlot. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SingularValuePlot.html

BibTeX

@misc{reference.wolfram_2026_singularvalueplot, author="Wolfram Research", title="{SingularValuePlot}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/SingularValuePlot.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_singularvalueplot, organization={Wolfram Research}, title={SingularValuePlot}, year={2014}, url={https://reference.wolfram.com/language/ref/SingularValuePlot.html}, note=[Accessed: 13-June-2026]}