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The 

ν

, i = 1,2,...,ns have been termed above the Hankel singular values of 

the phase matrix associated with G. The corresponding quantities for G

 are 

ν

, i = 1,..., nsr.

The introduction to this chapter emphasized the importance of the error 
measures

 or 

 

for plant reduction, as opposed to

 or 

The BST algorithm ensures that in addition to (Equation 3-2), there holds 
[WaS90a].

which also means that for a scalar system,

and, if the bound is small:

For square minimum phase but not necessarily stable G, it also is possible 
to use this algorithm (with minor modification) to try to minimize (for G

 

of a certain order) the error bound

–

(

)G

1

–

∞

1

–

–

(

)

–

(

)G

1

–

∞

1

–

–

(

)

∞

1

–

–

(

)

∞

2

1 v

–

-------------

nsr 1

+

=

∑

≤

20log

10

------

8.69

≤

2

1 v

–

-------------

nsr 1

+

=

∑

⎝

⎠

⎜

⎟

⎜

⎟

⎛

⎞

phase G

( ) phase G

( )

–

1 v

–

-------------

nsr 1

+

=

∑

≤

–

(

)G

1

–

∞