DiscreteLQRegulatorGains
DiscreteLQRegulatorGains[ssm,{q,r},τ]
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.
DiscreteLQRegulatorGains[ssm,{q,r,p},τ]
includes the state-control cross-coupling matrix p in the cost function.
DiscreteLQRegulatorGains[{ssm,finputs},{…},τ]
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]
Examples
open allclose allScope (3)
Applications (1)
Properties & Relations (1)
Compute the weights for the emulated discrete-time system:
Compute the discrete LQ gains using the emulated system and corresponding weights:
DiscreteLQRegulatorGains directly gives the same result:
Text
Wolfram Research (2010), DiscreteLQRegulatorGains, Wolfram Language function, https://reference.wolfram.com/language/ref/DiscreteLQRegulatorGains.html (updated 2012).
BibTeX
BibLaTeX
CMS
Wolfram Language. 2010. "DiscreteLQRegulatorGains." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2012. https://reference.wolfram.com/language/ref/DiscreteLQRegulatorGains.html.
APA
Wolfram Language. (2010). DiscreteLQRegulatorGains. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/DiscreteLQRegulatorGains.html