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arx2th
Purpose
Construct theta format matrix from ARX polynomials.
arx2th
Syntax
th = arx2th(A,B,ny,nu)
th = arx2th(A,B,ny,nu,lam,T)
Description
arx2th creates a matrix containing parameters that describe the general
multi-input, multi-output model structure of ARX type:
y ( t ) + A 1 y ( t – 1 ) + A 2 y ( t – 2 ) + … + A na y ( t – na ) =
B 0 u ( t ) + B 1 u ( t – 1 ) + … + B nb u ( t – nb ) + e ( t )
Here A k and B k are matrices of dimensions ny by ny and ny by nu, respectively
(ny is the number of outputs, i.e., the dimension of the vector y ( t ) and nu is the
number of inputs). “Defining Model Structures” on page 3-29.
The arguments A and B are matrices that contain the A matrices and the B
matrices of the model:
A = [I A1 A2 ... Ana]
B = [B0 B1 ... Bnb]
Note that A always starts with the identity matrix, and that delays in the model
are defined by setting the corresponding leading entries in B to zero. For a
multivariate time series take B = [].
The arguments ny and nu denote the number of outputs and inputs,
respectively.
The optional argument lam sets the covariance matrix of the driving noise
source e ( t ) in the model above. The default value is the identity matrix.
The optional argument T defines the sampling interval (Default 1).
th is returned as a model structure in the theta format. See theta.
The use of arx2th is twofold. You can use it to create models that are simulated
(using idsim) or analyzed (using th2ff, th2zp, etc.). You can also use it to
define initial value models that are further adjusted to data (using pem). The
free parameters in the structure are consistent with the structure of A and B,
i.e., leading zeros in the rows of B are regarded as fixed delays, and trailing
zeros in A and B are regarded as a definition of lower order polynomials. These
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