National Instruments Xmath

Chapter 1 Introduction

Certain restrictions regarding minimality and stability are required of the

input data, and are summarized in Table1-1.

Documentation of the individual functions sometimes indicates how the

restrictions can be circumvented. There are a number of model reduction

methods not covered here. These include:

• Padé Approximation

• Methods based on interpolating, or matching at discrete frequencies

Table 1-1. MRM Restrictions

balance( ) A stable, minimal system

balmoore ( ) A state-space system must be stable and minimal,

having at least one input, output, and state

bst( ) A state-space system must be linear,

continuous-time, and stable, with full rank along

the jω-axis, including infinity

compare( ) Must be a state-space system

fracred( ) A state-space system must be linear and continuous

hankelsv( ) A system must be linear and stable

mreduce( ) A submatrix of a matrix must be nonsingular

forcontinuous systems, and variant for discrete

systems

mulhank( ) A state-space system must be linear,

continuous-time, stable and square, with full

rank al ong the jω-axis, including infinity

ophank( ) A state-space system must be linear,

continuous-time and stable, but can be nonminimal

redschur( ) A state-space system must be stable and linear,

butcan be nonminimal

stable ( ) No restriction

truncate( ) Any full-order state-space system

wtbalance( ) A state-space system must be linear and

continuous. Interconnection of controller and plant

must be stable, and/or weight must be stable.