Estimate statespace model using a subspace method.
sys = n4sid(data,nx)
sys = n4sid(data,nx,Name,Value)
sys = n4sid(___,opt)
[sys,x0] = n4sid(___)
estimates
an sys
= n4sid(data
,nx
)nx
order statespace model, sys
,
using measured inputoutput data, data
.
sys
is an idss
model
representing the system:
$$\begin{array}{l}\dot{x}(t)=Ax(t)+Bu(t)+Ke(t)\\ y(t)=Cx(t)+Du(t)+e(t)\end{array}$$
A,B,C,
and D are statespace matrices. K is
the disturbance matrix. u(t)
is the input, y(t) is the output, x(t)
is the vector of nx
states and e(t)
is the disturbance.
All the entries of the A, B, C and K matrices
are free estimation parameters by default. D is
fixed to zero by default, meaning that there is no feedthrough, except
for static systems (nx=0
).
specifies
additional attributes of the statespace structure using one or more sys
= n4sid(data
,nx
,Name,Value
)Name,Value
pair
arguments. Use the Form
, Feedthrough
and DisturbanceModel
namevalue
pair arguments to modify the default behavior of the A, B, C, D,
and K matrices.
specifies
estimation options, sys
= n4sid(___,opt
)opt
, that configure the initial
states, estimation objective, and subspace algorithm related choices
to be used for estimation.
[
also
returns the estimated initial state.sys
,x0
] = n4sid(___)

Identified statespace model.


Initial states computed during the estimator of If 
[1] Ljung, L. System Identification: Theory for the User, Appendix 4A, Second Edition, pp. 132–134. Upper Saddle River, NJ: Prentice Hall PTR, 1999.
[2] van Overschee, P., and B. De Moor. Subspace Identification of Linear Systems: Theory, Implementation, Applications. Springer Publishing: 1996.
[3] Verhaegen, M. "Identification of the deterministic part of MIMO state space models." Automatica, 1994, Vol. 30, pp. 61—74.
[4] Larimore, W.E. "Canonical variate analysis in identification, filtering and adaptive control." Proceedings of the 29th IEEE Conference on Decision and Control, 1990, pp. 596–604.