National Instruments NI MATRIXx Xmath - Manual (Page 92)

© National Instruments Corporation 5-1 Xmath Model Reduction Module
5
Utilities
This chapter describes three utility functions: hankelsv( ) , stable( ) ,
and compare( ) .
The background to hankelsv( ) , which calculates Hankel singular
values, was presented in Chapter 1, Introduction . Hankel singular values
are also calculated in other functions, sometimes by other procedures.
A comparison of the procedures is given in the
Hankel Singular Values
section. The function compare( ) serves to facilitate the comparisons
of an unreduced and a reduced system, from various points of views.
The function stable( ) is used to separate (additively) a system into its
stable and unstable parts, that is, given G(s), the function determines G
s
(s)
and G
u
(s), the first with all poles in Re[s] < 0, the second with all poles in
Re[s]
≥ 0, such that
The function is used within some of the other functions of the Model
Reduction Module. It should also be used when reduction of an unstable
G(s) is contemplated. The normal reduction functions, for example,
balmoore( ) or redschur( ) , require stability of the transfer function
matrix G(s) being reduced. If G(s) is unstable, stable( ) should be used
to generate G
s
(s) and G
u
(s); reduction of G
s
(s) should be performed, and
then G
u
(s) added to the outcome using the + operator, to yield the desired
reduction of G
s
(s).
hankelsv( )
[HSV,Wc,Wo] = hankelsv(Sys,{noplot})
The hankelsv( ) function computes the Hankel Singular Values of a
stable system (continuous or discrete) and displays them in a bar plot.
G s ( ) G
s
s ( ) G
u
s ( )
+ =