User`s guide

3 Linear Model Identification
matrices A, B, C,andD, and the remaining matrix elements are xed to
zeros and ones.
Of the two popular canonical forms, which include controllable canonical
form and observable canonical form, the toolbox supports only controllable
forms. Controllable canonical structures include free parameters in output
rows of the A matrix, free B and K matrices, and the xed C matrix. The
representation within controllable canonical forms is not unique and the
exact form depends on the actual choices of canonical indices. For more
information about the distribution of free parameters in canonical forms, see
the appendix on identiability of black-box multivariable model structures in
System Identication: Theory for the User, Second Edition, by Lennart Ljung,
Prentice Hall PTR, 199 9 (equation 4A.16).
Estimating Canonical State-Space Models
You can estimate s tate-space models with canonical parameterization at the
command line.
To specify a canonical form for
A, B, C,andD,settheSSparameterization
model property directly in the estimator syntax, as follow s:
m = pem(data,n,'SSparameterization','canonical')
If you have time-domain data, the preceding command estimates a
discrete-time model.
Note When you estimate the D matrix in canonical form, you must set the nk
property. See “Choosing to E stimate D, K, and X0 Matrices” on page 3-89.
If you have continuous-time frequency-domain data, the preceding syntax
estimates an
nth order continuous-time state-space model with no direct
contribution from the input to the output (D=0). To include a D matrix, set
the
nk property to 0 in the estimation, as follows:
m = pem(data,n,'SSparameterization','canonical',
'nk',0)
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