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Singular values plot of dynamic system

`sigma(sys)sigma(sys,w)sigma(sys,[],type)sigma(sys,w,type)sigma(sys1,sys2,...,sysN,w,type)sigma(sys1,'PlotStyle1',...,sysN,'PlotStyleN',w,type)sv = sigma(sys,w)[sv,w]
= sigma(sys)`

`sigma ` calculates the singular values of the
frequency response of a dynamic system `sys`.
For an FRD model, `sigma` computes the singular values
of `sys.Response` 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}*,

for frequencies ω between 0 and the Nyquist frequency
ω* _{N}* = π/

The singular values of the frequency response extend the Bode
magnitude response for MIMO systems and are useful in robustness analysis.
The singular value response of a SISO system is identical to its Bode
magnitude response. When invoked without output arguments, `sigma` produces
a singular value plot on the screen.

`sigma(sys)` plots the singular
values of the frequency response of a model `sys`.
This model can be continuous or discrete, and SISO or MIMO. The frequency
points are chosen automatically based on the system poles and zeros,
or from `sys.frequency` if `sys` is
an FRD.

`sigma(sys,w)` explicitly
specifies the frequency range or frequency points to be used for the
plot. To focus on a particular frequency interval `[wmin,wmax]`,
set `w = {wmin,wmax}`. To use particular frequency
points, set `w` to the corresponding vector of frequencies.
Use `logspace` to generate logarithmically spaced
frequency vectors. Frequencies must be in `rad/TimeUnit`,
where `TimeUnit` is the time units of the input dynamic
system, specified in the `TimeUnit` property
of `sys`.

`sigma(sys,[],type)` or `sigma(sys,w,type)` plots
the following modified singular value responses:

| Singular values of the frequency response |

| Singular values of the frequency response |

| Singular values of the frequency response |

These options are available only for square systems, that is, with the same number of inputs and outputs.

`sigma(sys1,sys2,...,sysN,w,type)` plots
the singular value plots of several LTI models on a single figure.
The arguments `w` and `type` are
optional. The models `sys1,sys2,...,sysN `need not
have the same number of inputs and outputs. Each model can be either
continuous- or discrete-time.

`sigma(sys1,'PlotStyle1',...,sysN,'PlotStyleN',w,type)` specifies
a distinctive color, linestyle, and/or marker for each system plot.
See `bode` for an example.

`sv = sigma(sys,w)` and `[sv,w]
= sigma(sys)` return the singular values `sv` of
the frequency response at the frequencies `w`. For
a system with `Nu` input and `Ny` outputs,
the array `sv` has `min(Nu,Ny)` rows
and as many columns as frequency points (length of `w`).
The singular values at the frequency `w(k)` are given
by `sv(:,k)`.

**Singular
Values Plot of Dynamic System**

Plot the singular value responses of

and *I* + *H*(*s*).

You can do this by typing

H = [0 tf([3 0],[1 1 10]) ; tf([1 1],[1 5]) tf(2,[1 6])] subplot(211) sigma(H) subplot(212) sigma(H,[],2)

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