# era

Estimate state-space model from impulse response data using Eigensystem Realization Algorithm (ERA)

*Since R2022b*

## Description

`era`

uses the
Eigensystem
Realization Algorithm [1] to estimate a state-space
model using impulse response data rather than input/output data. `era`

is
especially useful for identifying dynamic systems for applications such as modal analysis or
structural health modeling.You can also use `era`

for modeling time-series
data for applications such as prediction. For more information about the algorithm, see [1].

estimates
a state-space model using the time-domain impulse response data in
`sys`

= era(`data`

)`data`

, which can be either a timetable or matrix that contains only
output data. The software determines the order of the model `nx`

automatically.

`sys`

is a model of the following form:

$$\begin{array}{l}\dot{x}(t)=Ax(t)+Bu(t)+Ke(t)\\ y(t)=Cx(t)+Du(t)+e(t)\end{array}$$

*A*, *B*, *C*, *D*,
and *K* are state-space matrices.
*u*(*t*) is the input,
*y*(*t*) is the output,
*e*(*t*) is the disturbance, and
*x*(*t*) is the vector of `nx`

states.

All entries of *A*, *B*, *C*, and
*K* are free estimable parameters by default. *D* is
fixed to zero by default, meaning that there is no feedthrough, except for static systems
(`nx = 0`

).

The software sets the sample time of `sys`

to the sample time of
`data`

if `data`

is a timetable, or to -1 if
`data`

is a matrix.

incorporates additional options specified by one or more name-value arguments. For example,
use the `sys`

= era(`data`

,`nx`

,`Name=Value`

)`Feedthrough`

name-value argument to introduce feedthrough by
estimating the *D* matrix. Use the `InputDelay`

name-value argument to specify input delays for each channel.

## Examples

## Input Arguments

## Output Arguments

## References

[1] Juang, Jer-Nan, and Richard S.
Pappa. “An Eigensystem Realization Algorithm for Modal Parameter Identification and Model
Reduction.” *Journal of Guidance, Control, and Dynamics* 8, no. 5
(September 1985): 620–27. https://doi.org/10.2514/3.20031.

## Version History

**Introduced in R2022b**