# ssregest

Estimate state-space model by reduction of regularized ARX model

## Syntax

## Description

### Estimate State-Space Model

estimates a discrete-time state-space model by reduction of a regularized ARX
model, using the all the input and output signals in the timetable
`sys`

= ssregest(`tt`

,`nx`

)`tt`

. You can use this syntax for SISO and MIMO systems.
The function assumes that the last variable in the timetable is the single
output signal. You can also use this syntax to estimate a time-series model if
`tt`

contains a single variable that represents the sole
output.

For MIMO systems and for timetables that contain more variables than you plan
to use for estimation, you must also use name-value arguments to specify the
names of the input and output channels you want. For more information, see
`tt`

.

To estimate a continuous-time model, set `'Ts'`

to
`0`

using name-value syntax.

uses the time-domain input and output signals in the comma-separated matrices
`sys`

= ssregest(`u`

,`y`

,`nx`

,`'Ts'`

,`Ts`

)`u`

,`y`

and the model sample time
`Ts`

. The software assumes that the data sample time is
also `Ts`

seconds. You can use this syntax for SISO, MISO,
and MIMO systems.

Estimating continuous-time models from matrix-based data is not recommended.

uses the time-domain or frequency-domain data in the data object
`sys`

= ssregest(`data`

,`nx`

)`data`

. Use this syntax especially when you want to
estimate a state-space model using frequency-domain or frequency-response data,
or when you want to take advantage of the additional information, such as data
sample time or experiment labeling, that data objects provide.

### Specify Additional Options

incorporates additional model options specified by one or more name-value
arguments. For example, specify input and output signal variable names that
correspond with the variables to use for MIMO timetable data using `sys`

= ssregest(___,`nx`

,`Name,Value`

)```
sys
=
ssregest(data,nx,'InputName',["u1","u2"],'OutputName',["y1","y3"])
```

.
Use the `'Form'`

, `'Feedthrough'`

, and
`'DisturbanceModel'`

name-value arguments to modify the
default behavior of the *A*, *B*,
*C*, *D*, and *K*
matrices.

## Examples

## Input Arguments

## Output Arguments

## More About

## Tips

`ssregest`

function provides improved accuracy than`n4sid`

for short, noisy data sets.For some problems, the quality of fit using

`n4sid`

is sensitive to options, such as`N4Horizon`

, whose values can be difficult to determine. In comparison, the quality of fit with`ssregest`

is less sensitive to its options, which makes`ssregest`

simpler to use.

## Algorithms

`ssregest`

estimates a regularized ARX model
and converts the ARX model to a state-space model. The software then
uses balanced model reduction techniques to reduce the state-space
model to the specified order.

## References

[1] Ljung, L. *System Identification:
Theory For the User*, Second Edition, Appendix 4A, pp 132-134,
Upper Saddle River, N.J: Prentice Hall, 1999.

## Version History

**Introduced in R2014a**