# 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 pi.

StateFeedbackGains[{ssm,{in1,}},]

specifies control inputs ini to use.

# Details 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 {p1,p2,,pn}, 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 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 and returned as a vector.
• StateFeedbackGains[{ssm,{in1,}},] is equivalent to StateFeedbackGains[ssm1,], where ssm1SystemsModelExtract[ssm,{in1,}].
• StateFeedbackGains accepts a Method option with settings given by:
•  Automatic automatic method selection "Ackermann" Ackermann method "KNVD" Kautsky–Nichols–Van Dooren method

# Examples

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## 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:

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