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Related functions, Compare( ), Related functions -4 – National Instruments NI MATRIXx Xmath User Manual

Page 95: Compare( ) -4

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Chapter 5

Utilities

Xmath Model Reduction Module

5-4

ni.com

After this last transformation, and with

it follows that

and

By combining the transformation yielding the real ordered Schur form for
A with the transformation defined using X, the overall transformation T is
readily identified. In case all eigenvalues of A are stable or all are unstable,
this is flagged, and T = I.

stable( )

can be combined with a reduction algorithm such as

redschur( )

or

balmoore( )

to reduce the order of a system with some

unstable and some stable poles. One uses

stable( )

to separate the stable

and unstable parts, and then, for example, reduces the stable part with

redschur( )

; the reduced stable part is added to the original unstable part

to provide the desired system reduction.

Related Functions

sylvester()

,

schur()

,

redschur()

,

balmoore()

compare( )

[respdiff] = compare(Sys,SysRed,FTvec,{Fmin,Fmax,npts,radians,type})

The

compare( )

function provides a number of different graphical tests

which can be used to compare two state-space system implementations.

compare( )

can be used as a tool for evaluating a reduced-order system

by comparing it with the original full-order system from which it was
obtained. However, it can be used for more general comparisons as well,
such as examining the results of different discretization or identification
techniques.

B

B

S

B

U

=

C

C

S

C

U

[

]

=

SysS

A

S

A

S

C

S

D

;

[

,

]

=

SysU

A

U

B

U

C

U

0

;

[

,

]

=