about“dordvarx”function a little question

[bin147258]

Issue Description

I've been working with the dordvarx function for system identification purposes, where I used the parameter noD=1 to indicate that the direct feedthrough term should not be considered in the estimated model. However, when I subsequently use the dx2abcdk function to obtain the state-space matrices (A, B, C, D) from the identified model, I noticed that the D matrix is not a zero matrix as expected. I'm seeking clarification on why this is happening and if there's a specific reason the direct term is still present in the D matrix.

Additionally, I'm interested in estimating models where the C matrix is an identity matrix. Could you provide guidance or suggestions on how to enforce or achieve a C matrix that is an identity matrix during the system identification process with these functions?

Steps to Reproduce

1. Use dordvarx function with noD=1 parameter to identify a model from time-series data.
2. Apply dx2abcdk function to the identified model to obtain state-space matrices.
3. Observe that the D matrix is not a zero matrix.

Expected Behavior

When setting noD=1 in the dordvarx function, I expect the resulting D matrix (obtained after applying dx2abcdk) to be a zero matrix, indicating no direct feedthrough term in the identified model.

Environment

• MATLAB version: MATLAB 2023b

Additional Context

Any insights or suggestions on how to estimate models with an identity matrix for C using these functions would also be greatly appreciated.

Thank you for your assistance.