# Wolfram Language & System 10.0 (2014)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE 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 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

## ExamplesExamplesopen allclose all

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

Place the poles at :

 Out[1]=

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

 Out[2]=
 Out[3]=

Eigenvalue assignment for a two-input system:

 Out[1]=

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

 Out[1]=