gives the optimal discrete-time state feedback gain matrix with sampling period τ for the continuous-time StateSpaceModel ssm and the quadratic cost function, with state and control weighting matrices q and r.


includes the state-control cross-coupling matrix p in the cost function.


specifies the feedback inputs of ssm.

Details and Options

  • The standard state-space model ssm can be given as StateSpaceModel[{a,b,}], where a and b represent the state and input matrices in the continuous-time system .
  • The descriptor continuous-time state-space model ssm defined by can be given as StateSpaceModel[{a,b,c,d,e}].
  • The argument finputs is a list of integers specifying the positions of the feedback inputs in .
  • DiscreteLQRegulatorGains[ssm,{},τ] is equivalent to DiscreteLQRegulatorGains[{ssm,All},{},τ].
  • The cost function is given by .
  • In DiscreteLQRegulatorGains[ssm,{q,r},τ], the cross-coupling matrix is assumed to be zero.
  • DiscreteLQRegulatorGains computes the regulator gains based on the emulated system with cost function .
  • The matrix is the submatrix of associated with the feedback inputs .
  • The emulated closed-loop system with the computed feedback gain matrix k can be obtained from SystemsModelStateFeedbackConnect[ToDiscreteTimeModel[ssm,τ,Method->"ZeroOrderHold"],k]


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Basic Examples  (1)

Compute a set of discrete-time regulator gains for a continuous-time system:

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Scope  (3)

Applications  (1)

Properties & Relations  (1)

Possible Issues  (1)

See Also

LQRegulatorGains  DiscreteLQEstimatorGains

Introduced in 2010
| Updated in 2012