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
open allclose allBasic Examples (4)
Scope (6)
Options (5)
Applications (5)
Properties & Relations (6)
Possible Issues (3)
See Also
LQRegulatorGains DiscreteLQRegulatorGains LQOutputRegulatorGains EstimatorGains LQGRegulator EstimatorRegulator SystemsModelStateFeedbackConnect ControllableModelQ
Related Guides
Introduced in 2010
(8.0)
| Updated in 2014 (10.0)