© 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 Chapter1, Introduction. Hankel singular values
are also calculated in other functions, sometimes by other procedures.
A comparison of the procedures is given in the Han kel Singular Values
section. The function compare( ) serves to facilitate the comparisons
ofan 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 Gs(s)
and Gu(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 Gs(s) and Gu(s); reduction of Gs(s) should be performed, and
then Gu(s) added to the outcome using the + operator, to yield the desired
reduction of Gs(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.
Gs() Gss() Gus()+=