Chapter 5 utilities, Hankelsv( ), Hankelsv( ) -1 – National Instruments NI MATRIXx Xmath User Manual

Page 92: Er 5, Utilities, Describ

5-1

Xmath Model Reduction Module

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)

and G

(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( )

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) and G

(s); reduction of G

(s) should be performed, and

then G

(s) added to the outcome using the + operator, to yield the desired

reduction of G

(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

( )