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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.

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.

stable()

, 

redschur()

, 

balmoore() 

( ) g

( )

–

1 2 2i 2

–

+

(

)σ

( )

σ

( )

+

∑

+

≤