BUILT-IN MATHEMATICA SYMBOL

# StateFeedbackGains

StateFeedbackGains[ssm, {p1, p2, ..., pn}]
gives the state feedback gain matrix for the state-space model ssm, such that the poles of the closed-loop system are .

StateFeedbackGains[{ssm, {in1, ...}}, ...]
specifies control inputs to use.

## Details and OptionsDetails and Options

• StateFeedbackGains is also known as pole placement gains.
• The state-space model ssm can be given as StateSpaceModel[{a, b, ...}], where a and b represent the state and input matrices in either a continuous-time or a discrete-time system:
•  continuous-time system discrete-time system
• If ssm is controllable, the eigenvalues of will be , where is the computed state feedback 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 controllability of the system.
• StateFeedbackGains[{ssm, {in1, ...}}, ...] is equivalent to StateFeedbackGains[ssm1, ...], where ssm1=SystemsModelExtract[ssm, {in1, ...}].
• StateFeedbackGains accepts a Method option with settings given by:
•  Automatic automatic method selection "Ackermann" Ackermann method "KNVD" Kautsky-Nichols-Van Dooren method

## ExamplesExamplesopen allclose all

### Basic Examples (4)Basic Examples (4)

Place the poles at :

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Place all the eigenvalues of a discrete-time system at the origin:

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Eigenvalue assignment for a two-input system:

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Calculate the feedback gains for a two-input system, using the first input:

 Out[1]=