© National Instruments Corporation v Xmath Model Reduction Module
Contents

Chapter 1

Introduction

Using This Manual.........................................................................................................1-1
Document Organization...................................................................................1-1
Bibliographic References................................................................................1-2
Commonly Used Nomenclature......................................................................1-2
Conventions.....................................................................................................1-2
Related Publications........................................................................................1-3
MATRIXx Help...............................................................................................1-3
Overview........................................................................................................................1-3
Functions.........................................................................................................1-4
Nomenclature .................................................................................................1-6
Commonly Used Concepts............................................................................................1-7
Controllability and Observability Grammians................................................1-7
Hankel Singular Values...................................................................................1-8
Internally Balanced Realizations.....................................................................1-10
Singular Perturbation.......................................................................................1-11
Spectral Factorization......................................................................................1-13
Low Order Controller Design Through Order Reduction.............................................1-15

Chapter 2

Additive Error Reduction

Introduction....................................................................................................................2-1
Truncation of Balanced Realizations.............................................................................2-2
Reduction Through Balanced Realization Truncation...................................................2-4
Singular Perturbation of Balanced Realization..............................................................2-5
Hankel Norm Approximation........................................................................................2-6
balmoore() .....................................................................................................................2-8
Related Functions............................................................................................2-11
truncate() .......................................................................................................................2-11
Related Functions............................................................................................2-11
redschur() ......................................................................................................................2-12
Algorithm........................................................................................................2-12
Related Functions............................................................................................2-14
ophank() ........................................................................................................................2-14
Restriction........................................................................................................2-14
Algorithm........................................................................................................2-15
Behaviors.........................................................................................................2-15