Hankel singular values of dynamic system

* hsv* = hsvd(

`sys`

`hsv`

`sys`

`opts`

[hsv,baldata] = hsvd(___)

hsvd(___)

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`

.

computes
the Hankel singular values using options that you specify using * hsv* = hsvd(

`sys`

`opts`

`hsvdOptions`

. Options include offset
and tolerance options for computing the stable-unstable decompositions.
The options also allow you to limit the HSV computation to energy
contributions within particular time and frequency intervals. See `hsvdOptions`

for details.`[hsv,baldata] = hsvd(___)`

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

. You can use this syntax with
any of the previous combinations of input arguments.

`hsvd(___)`

displays a Hankel
singular values plot.

[1] Gawronski, W. and J.N. Juang. "Model
Reduction in Limited Time and Frequency Intervals." *International
Journal of Systems Science*. Vol. 21, Number 2, 1990, pp.
349–376.

`balreal`

| `balred`

| `hsvdOptions`

| `hsvplot`

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