This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# DiscreteLQRegulatorGains

 DiscreteLQRegulatorGains gives the optimal discrete-time state feedback gain matrix with sampling period for the continuous-time StateSpaceModel object ss and the quadratic cost function with state and control weighting matrices q and r. DiscreteLQRegulatorGains includes the state-control cross-coupling matrix p in the cost function. DiscreteLQRegulatorGainsspecifies the feedback inputs of ss.
• The state-space model ss can be given as StateSpaceModel, where a and b represent the state and input matrices in the continuous-time system .
• The argument finputs is a list of integers specifying the positions of the feedback inputs in .
• The cost function is given by .
• The matrix is the submatrix of associated with the feedback inputs .
Compute a set of discrete-time regulator gains for a continuous-time system:
Compute a set of discrete-time regulator gains for a continuous-time system:
 Out[1]=
 Scope   (2)
Compute a set of discrete LQ regulator gains for a continuous-time state-space model:
Only use the first input as the feedback input:
Compute the gains with state-control coupling in the cost function:
Use only inputs 1 and 3 for feedback:
 Applications   (1)
Design an optimal controller by emulation:
The step response of the emulated system:
Use LQRegulatorGains and the discretized system and weighting matrices to compute the discrete LQ regulator gains:
DiscreteLQRegulatorGains directly gives the same result:
It is not possible to compute an optimal regulator for a system that is not stabilizable:
The second mode is not stabilizable:
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