# EstimatorGains

EstimatorGains[ssm,{p1,p2,,pn}]

gives the estimator gain matrix for the StateSpaceModel ssm, such that the poles of the estimator are pi.

EstimatorGains[{ssm,{out1,}},]

specifies the measured outputs outi 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 {p1,p2,,pn}, 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 also accepts nonlinear systems specified by AffineStateSpaceModel and NonlinearStateSpaceModel.
• For nonlinear systems, the operating values of state and input variables are taken into consideration, and the gains are computed based on the approximate Taylor linearization.
• EstimatorGains[{ssm,{out1,}},] is equivalent to EstimatorGains[ssm1,], where ssm1SystemsModelExtract[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 .
• 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.

# Examples

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## Basic Examples(3)

Compute estimator gains for a continuous-time system:

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A discrete-time system:

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Estimator gains for a two-output system with only the second output measured:

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