control.eigensys_realization

control.eigensys_realization(YY, r)[source]

Calculate ERA model based on impulse-response data.

This function computes a discrete-time system

$x[k+1] &= A x[k] + B u[k] \\\\ y[k] &= C x[k] + D u[k]$

of order $r$ for a given impulse-response data (see [1]).

The function can be called with 2 arguments:

sysd, S = eigensys_realization(data, r)
sysd, S = eigensys_realization(YY, r)

where data is a TimeResponseData object, YY is a 1D or 3D array, and r is an integer.

Parameters

YYarray_like: Impulse response from which the StateSpace model is estimated, 1D or 3D array.
dataTimeResponseData: Impulse response from which the StateSpace model is estimated.
rinteger: Order of model.
minteger, optional: Number of rows in Hankel matrix. Default is 2*r.
ninteger, optional: Number of columns in Hankel matrix. Default is 2*r.
dtTrue or float, optional: True indicates discrete time with unspecified sampling time and a positive float is discrete time with the specified sampling time. It can be used to scale the StateSpace model in order to match the unit-area impulse response of python-control. Default is True.
transposebool, optional: Assume that input data is transposed relative to the standard Time series data conventions. For TimeResponseData this parameter is ignored. Default is False.

Returns

sysStateSpace: State space model of the specified order.
Sarray: Singular values of Hankel matrix. Can be used to choose a good r value.

References

1: Samet Oymak and Necmiye Ozay, Non-asymptotic Identification of LTI Systems from a Single Trajectory. https://arxiv.org/abs/1806.05722

Examples

>>> T = np.linspace(0, 10, 100)
>>> _, YY = ct.impulse_response(ct.tf([1], [1, 0.5], True), T)
>>> sysd, _ = ct.eigensys_realization(YY, r=1)

>>> T = np.linspace(0, 10, 100)
>>> response = ct.impulse_response(ct.tf([1], [1, 0.5], True), T)
>>> sysd, _ = ct.eigensys_realization(response, r=1)