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DOC: Clarify process-noise input dimensions in LQE #1256

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DOC: Clarify process-noise input dimensions in LQE #1256

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11b9782
docs(stochsys): state LQE noise-input dimensions explicitly
huxiaoyi-ovo Oct 12, 2026
c369c46
docs(stochastic): explain G=B and QN input-channel covariance
huxiaoyi-ovo Oct 12, 2026
283f442
docs(stochastic): separate estimator guidance paragraphs
huxiaoyi-ovo Oct 12, 2026
e3636cf
docs(stochsys): specify supported state-space LQE input
huxiaoyi-ovo Oct 13, 2026
a91905a
docs(stochastic): correct discrete-time estimator references
huxiaoyi-ovo Oct 13, 2026
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docs(stochastic): explain G=B and QN input-channel covariance
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huxiaoyi-ovo committed Oct 12, 2026
commit c369c46fb1099f51a02d002035a15a270e9fe340
12 changes: 11 additions & 1 deletion doc/stochastic.rst
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Expand Up @@ -181,7 +181,17 @@ called in several forms:
* ``L, P, E = lqe(A, G, C, QN, RN, NN)``

where :code:`sys` is an :class:`LTI` object, and `A`, `G`, `C`, `QN`, `RN`,
and `NN` are 2D arrays of appropriate dimension. If :code:`sys` is a
and `NN` are 2D arrays of appropriate dimension.

For the state-space system form ``lqe(sys, QN, RN)``, the process noise
matrix :math:`G` is taken to be :code:`sys.B`. This models disturbances
entering through the system's input channels: ``QN`` must have shape
``(sys.ninputs, sys.ninputs)``, which may differ from the number of states.
The same convention applies to ``dlqe(sys, QN, RN)`` for discrete-time
systems. To model noise entering through a different matrix, specify
:math:`G` explicitly using the ``lqe(A, G, C, QN, RN)`` form (or ``dlqe``).
For example, use ``G = np.eye(sys.nstates)`` if independent disturbances
are modelled as entering every state derivative. If :code:`sys` is a
discrete-time system, the first two forms will compute the discrete
time optimal controller. For the second two forms, the :func:`dlqr`
function can be used. Additional arguments and details are given on
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