Option set for
opt = n4sidOptions
opt = n4sidOptions(Name,Value)
comma-separated pairs of
the argument name and
Value is the corresponding value.
Name must appear inside quotes. You can specify several name and value
pair arguments in any order as
N4Weight— Weighting scheme used for singular-value decomposition by the
Weighting scheme used for singular-value decomposition by the N4SID algorithm, specified as one of the following values:
'MOESP' — Uses the MOESP
algorithm by Verhaegen .
'CVA' — Uses the Canonical Variate
Algorithm by Larimore .
Estimation using frequency-domain data always uses
'SSARX' — A subspace identification
method that uses an ARX estimation based algorithm to compute the
Specifying this option allows unbiased estimates when using data that is collected in closed-loop operation. For more information about the algorithm, see .
'auto' — The estimating
function chooses between the
N4Horizon— Forward- and backward-prediction horizons used by the
'auto'(default) | vector
[r sy su]|
Forward- and backward-prediction horizons used by the N4SID algorithm, specified as one of the following values:
A row vector with three elements —
[r sy su], where
r is the maximum forward prediction
horizon, using up to
r step-ahead predictors.
sy is the number of past outputs, and
su is the number of past inputs that are
used for the predictions. See pages 209 and 210 in  for more information. These numbers can have a substantial
influence on the quality of the resulting model, and there are
no simple rules for choosing them. Making
matrix means that each row of
tried, and the value that gives the best (prediction) fit to
data is selected.
k is the number of guesses
[r sy su] combinations. If
you specify N4Horizon as a single column,
r = sy =
su is used.
'auto' — The software uses
an Akaike Information Criterion (AIC) for the selection of
OutputWeight— Weighting of prediction errors in multi-output estimations
'noise'| positive semidefinite symmetric matrix
Weighting of prediction errors in multi-output estimations, specified as one of the following values:
'noise' — Minimize , where E represents
the prediction error and
N is the number of data
samples. 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 (
— Minimize the trace of the weighted prediction error matrix
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.
W to specify the relative importance of outputs
in multiple-output models, or the reliability of corresponding data.
N is the number of data samples.
 — The software chooses
'noise' or using the identity matrix
This option is relevant only for multi-output models.
Advanced— Additional advanced options
Additional advanced options, specified as a structure with the
the maximum number of elements in a segment when input-output data
is split into segments.
MaxSize must be a positive integer.
opt = n4sidOptions;
Create an options set for
n4sid using the
'zero' option to initialize the state. Set the
opt = n4sidOptions('InitialState','zero','Display','on');
Alternatively, use dot notation to set the values of
opt = n4sidOptions; opt.InitialState = 'zero'; opt.Display = 'on';
 Larimore, W.E. “Canonical variate analysis in identification, filtering and adaptive control.” Proceedings of the 29th IEEE Conference on Decision and Control, pp. 596–604, 1990.
 Verhaegen, M. “Identification of the deterministic part of MIMO state space models.” Automatica, Vol. 30, 1994, pp. 61–74.
 Ljung, L. System Identification: Theory for the User. Upper Saddle River, NJ: Prentice-Hall PTR, 1999.
 Jansson, M. “Subspace identification and ARX modeling.” 13th IFAC Symposium on System Identification, Rotterdam, The Netherlands, 2003.