National Instruments Xmath

Chapter 2 Additive Error Reduction

and finally:

These four matrices are the constituents of the system matrix of ,

where:

Digression:

This choice is related to the ideas of [Glo84] in the following way;

in [ Glo8 4], the complete set is identified of satisfying

with having a stable part of order ni–1

. The set is parameterized in

terms of a stable transfer function matrix K(s) which has to satisfy

with C2, B2 being two matrices appearing in the course of the algorithm

of [Glo84], and enjoying the property . The particular

choice

in the algorithm of [Glo84] and flagged in corollary 7.3 of [Glo84] is

equivalent to the previous construction, in the sense of yielding the

same , though the actual formulas used here and in [Glo84] for the

construction procedure are quite different. In a number of situations,

including the case of scalar (SISO)G(s), this is the only choice.

The next step of the algorithm is to call stable( ), to separate into

its stable and unstable parts, call them and , stable( ) will

always assign the matrix to , and the final step of the algorithm is

˜SB

1–A11 A12–A22

#A21

–()=

˜SB

1–B1A12–A22

#B2

–()=

˜C1C2A22

#A21

–=

˜DC

2A22

#B2

–=

˜s()

˜s() Grs() Gus()+=

˜s()

Gjω()G

˜jω()–∞σni

C2Ks()B2

′

+0=

IK′jω–()Kjω()–0forallω≤

′C2B2B2

′

Ks() C2C′2C2

()

#B2

–=

˜s

˜s()

˜s() G

˜us()

˜G

˜rs()