National Instruments NI MATRIXx Xmath - Manual (Page 28)

Chapter 2 Additive Error Reduction
© National Instruments Corporation 2-5 Xmath Model Reduction Module
order model is not one in general obtainable by truncation of an
internally-balanced realization of the full order model.
Figure 2-1 sets out several routes to a reduced-order realization. In
continuous time, a truncation of a balanced realization is again balanced.
This is not the case for discrete time, but otherwise it looks the same.
Figure 2-1. Different Approaches for Obtaining the Same Reduced Order Model
Singular Perturbation of Balanced Realization
Singular perturbation of a balanced realization is an attractive way to
produce a reduced order model. Suppose G(s) is defined by,
Full Order Realization
Balanced Realization of
Reduced Order Model
(in continuous time)
Nonbalanced
Realization of
Reduced Order Model Transfer Function
Reduced Order Model
balmoore
(with first step)
balance redschur
balmoore
(with both steps)
truncate
x·
1
x·
2
A
11
A
12
A
21
A
22
x
1
x
2
B
1
B
2
u
+ =
y C
1
C
2
x Du + =