© National Instruments Corporation I-1 Xmath Model Reduction Module
Index

Symbols

*, 1-6
´, 1-6

A

additive error, reduction, 2-1
algorithm
balanced stochastic truncation (bst), 3-4
fractional representation reduction, 4-18
Hankel multi-pass, 2-20
optimal Hankel norm reduction, 2-15
stable, 5-2
weighted balance, 4-12
all-pass transfer function, 1-6, 2-4

B

balance, 1-5, 2-4
algorithm, 1-11
balanced realization
definition, 1-10
internally balanced, 3-9
singular perturbation, 2-5
truncation, 2-2, 2-4
balanced stochastic truncation, 3-3
See also bst
balmoore, 1-5, 2-4
algorithm, 1-10
bst, 1-5, 1-14, 3-3

C

compare, 1-5, 5-4
controller reduction, 4-2
with fractional representations, 4-5
controller robustness, 4-2
conventions used in the manual, iv

D

diagnostic tools (NI resources), B-1
documentation
conventions used in the manual, iv
NI resources, B-1
drivers (NI resources), B-1

E

equality bounds, tight, 1-7
error bound, 2-7
for balanced stochastic truncation, 3-8
for balanced truncation, 2-2
for impulse responses, 2-3
for multiplicative Hankel reduction, 3-16
for stochastic truncation, 3-9
error formulas, ophank, 2-22
error reduction
additive, 2-1
frequency weighted, 1-1, 4-1
multiplicative, 1-1, 3-1
examples (NI resources), B-1

F

for Hankel norm approximation, 2-7
fracred, 1-5, 4-15
reduction, 4-18
frequency weighted error reduction, 1-1, 4-1
controller reduction, 4-2