Hankel singular values of dynamic system

* hsv* = hsvd(

`sys`

`hsv`

`sys`

`ATOL`

`RTOL`

`ALPHA`

`hsv`

`sys`

`opts`

hsvd(sys)

[hsv,baldata] = hsvd(sys)

computes
the Hankel singular values * hsv* = hsvd(

`sys`

`hsv`

of the dynamic
system `sys`

. In state coordinates that equalize
the input-to-state and state-to-output energy transfers, the Hankel
singular values measure the contribution of each state to the input/output
behavior. Hankel singular values are to model order what singular
values are to matrix rank. In particular, small Hankel singular values
signal states that can be discarded to simplify the model (see `balred`

).For models with unstable poles, `hsvd`

only
computes the Hankel singular values of the stable part and entries
of `hsv`

corresponding to unstable modes are set
to `Inf`

.

specifies
additional options for the stable/unstable decomposition. See the * hsv* = hsvd(

`sys`

`ATOL`

`RTOL`

`ALPHA`

`stabsep`

reference page for more information
about these options. The default values are `ATOL = 0`

, ```
RTOL
= 1e-8
```

, and `ALPHA = 1e-8`

.

computes
the Hankel singular values using the options specified in the * hsv* = hsvd(

`sys`

`opts`

`hsvdOptions`

object `opts`

.`hsvd(sys)`

displays a Hankel singular values
plot.

`[hsv,baldata] = hsvd(sys)`

returns additional
data to speed up model order reduction with `balred`

.
For example

sys = rss(20); % 20-th order model [hsv,baldata] = hsvd(sys); rsys = balred(sys,8:10,'Balancing',baldata); bode(sys,'b',rsys,'r--')

computes three approximations of `sys`

of orders
8, 9, 10.

There is more than one `hsvd`

available. Type

help lti/hsvd

for more information.

**Compute Hankel Singular Values**

This example illustrates how to compute Hankel singular values.

First, create a system with a stable pole very near to 0, then calculate the Hankel singular values.

sys = zpk([1 2],[-1 -2 -3 -10 -1e-7],1) hsvd(sys) Zero/pole/gain: (s-1) (s-2) ----------------------------------- (s+1) (s+2) (s+3) (s+10) (s+1e-007)

For a better view of the Hankel singular values, switch the
plot to log scale by selecting **Y Scale** > **Log** from the right-click menu.

Notice the dominant Hankel singular value with 1e5 magnitude,
due to the mode `s=-1e-7`

near the imaginary axis.
Set the `offset=1e-6`

to treat this mode as unstable

hsvd(sys,'Offset',1e-7)

The dominant Hankel singular value is now shown as unstable.

`balreal`

| `balred`

| `hsvdOptions`

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