National Instruments NI MATRIXx Xmath - Manual (Page 46)

Chapter 2 Additive Error Reduction
© National Instruments Corporation 2-23 Xmath Model Reduction Module
It follows by a result of [BoD87] that the impulse response error for t > 0
satisfies:
Evidently, Hankel norm approximation ensures some form of
approximation of the impulse response too.
Unstable System Approximation
A transfer function G(s) with stable and unstable poles can be reduced by
applying
stable( ) to separate G(s) into a stable and unstable part. The
former is reduced and then the unstable part can be added back on. For
additional information about the
ophank( ) function, refer to the Xmath
Help.
Related Functions
stable() , redschur() , balmoore()
g t ( ) g
r
t ( )
– 1 2 2i 2 – r +
( )σ
i
G ( ) σ
j
G ( )
i r +
ns
∑
+
≤