Estimates the A and C matrix in a discrete-time state-space model from time-domain data that was preprocessed by dordpi.


[A,C] = dmodpi(R,n) [A,C] = dmodpi(R,n,'stable')


This function estimates the A and C matrices corresponding to an n th order discrete-time LTI state-space model. The compressed data matrix R from the preprocessor function dordpi is used to this end.


R is a compressed data matrix containing information about the measured data, as well as information regarding the system dimensions.

n is the desired model order n.

stable estimates a stable A matrix, see[1].


A is the state-space model's A matrix.

C is the state-space model's C matrix.


The data matrix obtained with dordpi contains the weighted left singular vectors of the R32 matrix. The first n of these vectors form an estimate Os of the system's extended observability matrix:

The estimates Ahat and Chat are obtained by linear regression:

$$ \hat{C} = \hat{\mathcal{O}}_s(1:\ell,:) $$

$$ \hat{A} = \hat{\mathcal{O}}_s(1:(s-1)\ell,:)^\dagger
\hat{\mathcal{O}}_s(\ell+1:s\ell,:) $$

Used By

This a top-level function that is used directly by the user.

See Also

dordpo, dmodpo, dordpi, dordrs, dmodrs


[1] J.M. Maciejowski, "Guaranteed Stability with Subspace Methods",
Submitted to Systems and Control Letters, 1994.