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

# LQGRegulator

 LQGRegulator constructs the optimal feedback regulator for the StateSpaceModel ss using noisy measurements sensors and feedback inputs finputs. The process, measurement, and cross-covariance matrices are w, v, and h; and the state, input, and state-input weighting matrices are q, r, and p. LQGRegulatorspecifies einputs as the exogenous deterministic inputs.
• The state-space model ss can be given as StateSpaceModel, where a, b, c, and d represent the state, input, output, and transmission matrices in either a continuous-time or a discrete-time system:
 continuous-time system discrete-time system
• The input can include stochastic inputs , feedback inputs , and exogenous deterministic inputs .
• The arguments finputs and einputs are lists of integers specifying the positions of and in .
• The output consists of the noisy measurements as well as other outputs.
• The argument sensors is a list of integers specifying the positions of in .
• If not specified, h and p are assumed to be zero matrices.
• Block diagram of the continuous-time system with its regulator:
• Block diagram of the discrete-time system with its regulator:
• The system with the regulator has the following block diagram:
Construct an LQG regulator for a system with one measured output and one feedback input:
Construct an LQG regulator for a system with one measured output and one feedback input:
 Out[1]=
 Scope   (3)
An LQG regulator for a continuous-time system with one measurement and two feedback inputs:
An LQG regulator for a system with two sensor outputs, one feedback input, one exogenous deterministic input, and one stochastic input:
Design an LQG regulator for a discrete-time system:
 Applications   (1)
An LQG regulator for a SISO system:
The closed-loop system:
The closed-loop output response:
The closed-loop poles are the poles of the state-feedback and estimator subsystems:
Construct an LQG regulator from the optimal state-feedback gains and the Kalman estimator model:
LQGRegulator gives the same result:
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