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dlqe should return Kalman filter gain rather than Kalman predictor gain #1173

@dakeprithvi

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@dakeprithvi

Hi!
Firstly, thanks for the python control library. It has been quite useful to make a shift from Matlab to python.

I noticed that dlqe currently returns the predictor gain ($\tilde{L}$). I understand the intention is to use dare within dlqe to return the dual equivalent of the LQR gain. However, what if $A$ is not full rank and one wants to use the filter form? In that case, I can't do $L = A^{-1} \tilde{L}$.

Here are my definitions:
Filter form $L = PC^T (CPC^T + R)^{-1}$
Predictor form $\tilde{L} = APC^T (CPC^T + R)^{-1}$

Would it be possible to return the filter gain by default or offer an option to select the form?

Thanks,
Prithvi

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