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BUILT-IN MATHEMATICA SYMBOL
EstimatorGains
EstimatorGains[ssm, {p1, p2, ..., pn}]
gives the estimator gain matrix for the StateSpaceModel ssm, such that the poles of the estimator are 
.
EstimatorGains[{ssm, {out1, ...}}, ...]
specifies the measured outputs 
to use.
Details and Options
- EstimatorGains is also known as observer gains or observer pole placement.
- The state-space model ssm can be given as StateSpaceModel[{a, b, c, d}], where a, b, c, and d represent the state, input, output, and transmission matrices in either a continuous-time or a discrete-time system:
-
continuous-time system 
discrete-time system - If ssm is observable, the eigenvalues of
will be 
, where 
is the computed estimator gain matrix. - For a descriptor system StateSpaceModel[{a, b, c, d, e}], the number of poles that can be specified is determined by the rank of e and the observability of the system.
- EstimatorGains[{ssm, {out1, ...}}, ...] is equivalent to EstimatorGains[ssm1, ...], where ssm1=SystemsModelExtract[ssm, All, {out1, ...}].
- The observer dynamics are given by:
-
continuous-time system 
discrete-time system - In the case of a square nonsingular matrix
, the state vector can be computed as ![x=TemplateBox[{c}, Inverse].(y-d.u)](Files/EstimatorGains.en/11.png "x=TemplateBox[{c}, Inverse].(y-d.u)")
. - EstimatorGains accepts a Method option with settings given by:
-
Automatic automatic method selection "Ackermann" Ackermann method "KNVD" Kautsky-Nichols-Van Dooren method - The estimator gains are computed as the state feedback gains of the dual system.
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