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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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13 changes: 9 additions & 4 deletions control/stochsys.py
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Original file line number Diff line number Diff line change
Expand Up @@ -65,16 +65,17 @@ def lqe(*args, symmetric_kwargs=None, **kwargs):
* ``L, P, E = lqe(A, G, C, QN, RN)``
* ``L, P, E = lqe(A, G, C, QN, RN, NN)``

where `sys` is an `LTI` object, and `A`, `G`, `C`, `QN`, `RN`, and `NN`
are 2D arrays or matrices of appropriate dimension.
where `sys` is a `StateSpace` object, and `A`, `G`, `C`, `QN`, `RN`, and
`NN` are 2D arrays or matrices of appropriate dimension.

Parameters
----------
A, G, C : 2D array_like
Dynamics, process noise (disturbance), and output matrices.
sys : `StateSpace` or `TransferFunction`
sys : `StateSpace`
Linear I/O system, with the process noise input taken as the system
input.
input (`G = sys.B`). Thus `QN` must be square with dimension
`sys.ninputs`, not necessarily `sys.nstates`.
QN, RN : 2D array_like
Process and sensor noise covariance matrices.
NN : 2D array, optional
Expand Down Expand Up @@ -219,6 +220,10 @@ def dlqe(*args, symmetric_kwargs=None, **kwargs):
Process and sensor noise covariance matrices.
NN : 2D array, optional
Cross covariance matrix (not yet supported).
sys : `StateSpace`
If a state-space system is passed instead of `A`, `G`, and `C`,
its input matrix `sys.B` is used as `G`. Consequently `QN`
must have shape (`sys.ninputs`, `sys.ninputs`).
method : str, optional
Set the method used for computing the result. Current methods are
'slycot' and 'scipy'. If set to None (default), try 'slycot'
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23 changes: 17 additions & 6 deletions doc/stochastic.rst
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Expand Up @@ -180,12 +180,23 @@ called in several forms:
* ``L, P, E = lqe(A, G, C, QN, RN)``
* ``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
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
the :func:`lqr` and :func:`dlqr` documentation pages.
where :code:`sys` is a :class:`StateSpace` object, and `A`, `G`, `C`,
`QN`, `RN`, 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 call
:func:`dlqe` to compute the discrete-time estimator. For the matrix
forms, call :func:`dlqe` directly. Additional arguments and details
are given on the :func:`lqe` and :func:`dlqe` documentation pages.

.. testsetup:: kalman

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