Model order reduction

* rsys* = balred(

`sys`

`ORDERS`

`rsys`

`sys`

`ORDERS`

`BALDATA`

`rsys`

`opts`

computes
a reduced-order approximation * rsys* = balred(

`sys`

`ORDERS`

`rsys`

of the LTI model `sys`

.
The desired order (number of states) for `rsys`

is
specified by `ORDERS`

. You can try multiple orders
at once by setting `ORDERS`

to a vector of integers,
in which case `rsys`

is a vector of reduced-order
models. `balred`

uses implicit balancing techniques
to compute the reduced- order approximation `rsys`

.
Use `hsvd`

to plot the Hankel
singular values and pick an adequate approximation order. States with
relatively small Hankel singular values can be safely discarded.When `sys`

has unstable poles, it is first
decomposed into its stable and unstable parts using `stabsep`

, and only the stable part is
approximated. Use `balredOptions`

to
specify additional options for the stable/unstable decomposition.

When you have System Identification Toolbox™ software
installed, `sys`

can only be an identified state-space
model (`idss`

). The reduced-order model is also an `idss`

model.

uses
balancing data returned by * rsys* = balred(

`sys`

`ORDERS`

`BALDATA`

`hsvd`

.
Because `hsvd`

does most of the work needed to compute `rsys`

,
this syntax is more efficient when using `hsvd`

and `balred`

jointly.

computes
the model reduction using options that you specify using * rsys* = balred(___,

`opts`

`balredOptions`

. Options include offset
and tolerance options for computing the stable-unstable decompositions.
There also options for emphasizing particular time or frequency intervals.
See `balredOptions`

for details.**Note**

The order of the approximate model is always at least the number
of unstable poles and at most the minimal order of the original model
(number `NNZ`

of nonzero Hankel singular values using
an eps-level relative threshold)

[1] Varga, A., "Balancing-Free Square-Root Algorithm for Computing Singular Perturbation Approximations," Proc. of 30th IEEE CDC, Brighton, UK (1991), pp. 1062-1065.