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balance()

, 

truncate()

, 

redschur()

, 

mreduce()

SysR = truncate(Sys,nsr,{VD,VA})

The 

truncate( )

 function reduces a system 

Sys

 by retaining the first 

nsr

 states and throwing away the rest to form a system 

SysR

. 

If for 

Sys

 one has,

the reduced order system (in both continuous-time and discrete-time cases) 
is defined by A

11

, B

1

, C

1

, and D. If 

Sys

 is balanced, then 

SysR

 is an 

approximation of 

Sys

 achieving a certain error bound. 

truncate( )

 may 

well be used after an initial application of 

balmoore( )

 to further reduce 

a system should a larger approximation error be tolerable. Alternatively, it 
may be used after an initial application of 

balance( )

 or 

redschur( )

. 

If 

Sys

 was calculated from 

redschur( )

 and 

VA,VD

 were posed as 

arguments, then 

SysR

 is calculated as in 

redschur( )

 (refer to the 

 section).

truncate( )

 should be contrasted with 

mreduce( )

, which achieves a 

reduction through a singular perturbation calculation. If 

Sys

 is balanced, 

the same error bound formulas apply (though not necessarily the same 
errors), 

truncate( )

 always ensures exact matching at s =

∞ (in the 

continuous-time case), or exacting matching of the first impulse response 
coefficient D (in the discrete-time case), while 

mreduce( )

 ensures 

matching of DC gains for 

Sys

 and 

SysR

 in both the continuous-time and 

discrete-time case. For a additional information about the 

truncate( )

 

function, refer to the Xmath Help.

balance()

, 

balmoore()

, 

redschur()

, 

mreduce()

11

12

21

22

=

1

2

=

1

2

=