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There is one potential source of failure of the algorithm. Because G(s) is 
stable, 

 certainly will be, as its poles will be in the left half plane circle 

on diameter 

. If 

 acquires a pole outside this circle 

(but still in the left half plane of course)—and this appears possible in 
principle—G

(s) will then acquire a pole in Re [s] > 0. Should this difficulty 

be encountered, a smaller value of 

ε should be used.

redschur()

, 

mulhank()

[SysR,HSV] = mulhank(Sys,{nsr,left,right,bound,method})

The 

mulhank( )

 function calculates an optimal Hankel norm reduction of 

Sys

 for the multiplicative case.

This function has the following restrictions:

•

The user must ensure that the input system is stable and nonsingular at 
s = infinity.

•

The algorithm may be problematic if the input system has a zero on the 
j

ω-axis.

•

Only continuous systems are accepted; for discrete systems use 

makecontinuous( )

 before calling 

mulhank( )

, then discretize 

the result.

Sys=mulhank(makecontinuous(SysD));

SysD=discretize(Sys);

The objective of the algorithm, like 

bst( )

, is to approximate a high order 

square stable transfer function matrix G(s) by a lower order G

(s) with 

either 

 or 

 (approximately) minimized, 

under the constraint that G

 is stable and of prescribed order. 

The algorithm has the property that right half plane zeros of G(s) are 
retained as zeros of G

r

(s). This means that if G(s) has order NS with N

+

 

zeros in Re[s] > 0, G

r

(s) must have degree at least N

+

—else, given that it 

has N

+

 zeros in Re[s] > 0 it would not be proper, [GrA89]. 

G˜ s

( )

ε

–

j0 0

,

=

(

)

G˜

( )

–

(

)G

1

–

∞

1

–

–

(

)

∞