BUILT-IN MATHEMATICA SYMBOL

# DiscreteLQRegulatorGains

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]

## ExamplesExamplesopen allclose all

### Basic Examples (1)Basic Examples (1)

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

 Out[1]=