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

DiscreteLQRegulatorGains[ssm, {q, r, p}, ]
includes the state-control cross-coupling matrix p in the cost function.

DiscreteLQRegulatorGains[{ssm, finputs}, {...}, ]
specifies the feedback inputs of ssm.

Details and OptionsDetails 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, {...}, ] is equivalent to DiscreteLQRegulatorGains[{ssm, All}, {...}, ].
  • The cost function is given by .
  • In DiscreteLQRegulatorGains[ssm, {q, r}, ], 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, , Method->"ZeroOrderHold"], k]
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