System Identification Toolbox™

ssdata - State-space matrices from idmodel object

Syntax

[A,B,C,D,K,X0] = ssdata(m)
[A,B,C,D,K,X0,dA,dB,dC,dD,dK,dX0] = ssdata(m)

Description

m is the model given as any idmodel object. A, B, C, D, K, and X0 are the matrices in the state-space description

where is or depending on whether m is a continuous-time or discrete-time model.

dA, dB, dC, dD, dK, and dX0 are the standard deviations of the state-space matrices.

If the underlying model itself is a state-space model, the matrices correspond to the same basis. If the underlying model is an input-output model, an observer canonical form representation is obtained.

For a time-series model (no measured input channels, u = []), B and D are returned as the empty matrices.

Subreferencing models in the usual way (see idmodel properties) will give the state-space representation of the chosen channels. Notice in particular that

[A,B,C,D] = ssdata(m('m')) 

gives the response from the measured inputs. This is a model without a disturbance description. Moreover,

[A,B,C,D,K] = ssdata(m('n'))

('n' as in "noise") gives the disturbance description, that is, a time-series description of the additive noise with no measured inputs, so that B = [] and D = [].

To obtain state-space descriptions that treat all input channels, both u and e, as measured inputs, first apply the conversion

m = noisecnv(m)

or

m = noisecnv(m,'norm')

where the latter case first normalizes e to v, where v has a unit covariance matrix. See the reference page for noisecnv.

Algorithm

The computation of the standard deviations in the input-output case assumes that an A polynomial is not used together with an F or D polynomial in the general polynomial equation (see What Are Black-Box Polynomial Models?. For the computation of standard deviations in the case that the state-space parameters are complicated functions of the parameters, the Gauss approximation formula is used together with numerical derivatives. The step sizes for this differentiation are determined by nuderst.

See Also

ss

step