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Chapter 16
Using Stochastic System Models
The following equations define continuous and discrete stochastic
state-space models.
Continuous Stochastic State-Space Model
x· ( t ) = Ax ( t ) + Bu ( t ) + Gw ( t )
y ( t ) = Cx ( t ) + Du ( t ) + Hw ( t ) + v ( t )
Discrete Stochastic State-Space Model
x ( k + 1 ) = Ax ( k ) + Bu ( k ) + Gw ( k )
y ( k ) = Cx ( k ) + Du ( k ) + Hw ( k ) + v ( k )
Table 16-1 describes these variables.
Table 16-1. Dimensions and Names of Stochastic State-Space Model Variables
Variable
Dimension
Name
q
—
Length of process noise vector w.
r
—
Number of outputs.
n
—
Number of states.
w
q × 1 vector
Process noise vector.
v
r × 1 vector
Measurement noise vector.
G
n × q matrix
Weighting matrix relating the
process noise vector w to the
system states.
H
r × q matrix
Weighting matrix relating the
process noise vector w to the
system outputs.
Refer to the Constructing State-Space Models section of Chapter 2,
Constructing Dynamic System Models, for information about the A, B, C,
D, x, u, and y variables.
Use the CD Construct Stochastic Model VI to construct a stochastic
state-space model. Refer to the LabVIEW Help, available by selecting
Help»Search the LabVIEW Help, for information about this VI.
Control Design User Manual
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