Specify optional comma-separated pairs of Name,Value arguments.
Name is the argument
name and Value is the corresponding
value. Name must appear
inside single quotes (' ').
You can specify several name and value pair
arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: opt = ssregestOptions('InitialState','zero') fixes
the value of the initial states to zero.

ARX model orders, specified as a matrix of nonnegative integers [na
nb nk]. The max(ARXOrder)+1 must be greater
than the desired state-space model order (number of states). If you
specify a value, it is recommended that you use a large value for nb order.
To learn more about ARX model orders, see arx.

Options for model order reduction, specified as a structure
with the following fields:

StateElimMethod — State
elimination method. Specifies how to eliminate the weakly coupled
states (states with smallest Hankel singular values). Specified as
one of the following values:

'MatchDC'

Discards the specified states and alters the remaining states
to preserve the DC gain.

'Truncate'

Discards the specified states without altering the remaining
states. This method tends to product a better approximation in the
frequency domain, but the DC gains are not guaranteed to match.

Default:'Truncate'

AbsTol, RelTol — Absolute
and relative error tolerance for stable/unstable decomposition. Positive
scalar values. For an input model G with unstable
poles, balred first extracts the stable dynamics
by computing the stable/unstable decomposition G → GS + GU. The AbsTol and RelTol tolerances
control the accuracy of this decomposition by ensuring that the frequency
responses of G and GS + GU differ by no more than AbsTol + RelTol*abs(G).
Increasing these tolerances helps separate nearby stable and unstable
modes at the expense of accuracy. See stabsep for
more information.

Default:AbsTol =
0; RelTol = 1e-8

Offset — Offset for the
stable/unstable boundary. Positive scalar value. In the stable/unstable
decomposition, the stable term includes only poles satisfying

Estimation focus that defines how the errors e between
the measured and the modeled outputs are weighed at specific frequencies
during the minimization of the prediction error, specified as one
of the following:

'prediction' — Automatically
calculates the weighting function as a product of the input spectrum
and the inverse of the noise model. The weighting function minimizes
the one-step-ahead prediction, which typically favors fitting small
time intervals (higher frequency range). From a statistical-variance
point of view, this weighting function is optimal. This option focuses
on producing a good predictor.

'simulation' — Estimates
the model using the frequency weighting of the transfer function that
is given by the input spectrum. Typically, this method favors the
frequency range where the input spectrum has the most power.

Passbands — Row vector or matrix containing
frequency values that define desired passbands. For example:

[wl,wh]
[w1l,w1h;w2l,w2h;w3l,w3h;...]

where wl and wh represent
upper and lower limits of a passband. For a matrix with several rows
defining frequency passbands, the algorithm uses union of frequency
ranges to define the estimation passband.

SISO filter — Enter any SISO linear filter
in any of the following ways:

A single-input-single-output (SISO) linear system.

The {A,B,C,D} format, which specifies
the state-space matrices of the filter.

The {numerator, denominator} format,
which specifies the numerator and denominator of the filter transfer
function

This format calculates the weighting function as a product of
the filter and the input spectrum to estimate the transfer function.
To obtain a good model fit for a specific frequency range, you must
choose the filter with a passband in this range. The estimation result
is the same if you first prefilter the data using idfilt.

Weighting vector — For frequency-domain data
only, enter a column vector of weights for 'Focus'.
This vector must have the same size as length of the frequency vector
of the data set, Data.Frequency. Each input and
output response in the data is multiplied by the corresponding weight
at that frequency.

Higher weighting at specific frequencies emphasizes the requirement
for a good fit at these frequencies.

Specifies criterion used during minimization, specified as one
of the following:

'noise' — Minimize $$\mathrm{det}(E\text{'}*E)$$, where E represents
the prediction error. This choice is optimal in a statistical sense
and leads to the maximum likelihood estimates in case no data is available
about the variance of the noise. This option uses the inverse of the
estimated noise variance as the weighting function.

Positive semidefinite symmetric matrix (W)
— Minimize the trace of the weighted prediction error matrix trace(E'*E*W). E is
the matrix of prediction errors, with one column for each output. W is
the positive semidefinite symmetric matrix of size equal to the number
of outputs. Use W to specify the relative importance
of outputs in multiple-input, multiple-output models, or the reliability
of corresponding data.

This option is relevant only for multi-input, multi-output models.

[] — The software chooses
between the 'noise' or using the identity matrix
for W.

Maximum allowable size of Jacobian matrices and choice of search
method, specified as a structure with the following fields:

MaxSize — Maximum allowable
size of Jacobian matrices formed during estimation, specified as a
large positive number.

Default:250e3

SearchMethod — Search method
for estimating regularization parameters, specified as one of the
following strings:

'fmincon': Trust-region-reflective
constrained minimizer. In general, 'fmincon' is
better than 'gn' for handling bounds on regularization
parameters that are imposed automatically during estimation. Requires Optimization Toolbox™ software.

'gn': Quasi-Newton line search

Default:'fmincon'

If you do not have the Optimization Toolbox software, the
default is 'gn'.

Estimation options for ssregest, returned
as an ssregestOptions options
set.

References

[1] T. Chen, H. Ohlsson, and L. Ljung. "On
the Estimation of Transfer Functions, Regularizations and Gaussian
Processes - Revisited", Automatica,
Volume 48, August 2012.