National Instruments 370755B-01 truncate( )

Chapter 2 Additive Error Reduction

Related Functions

balance(), truncate(), redschur(), mreduce()

truncate( )

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 A11, B1, C1, 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

redschur() section).

truncate( ) should be contrasted with mreduce( ), which achieves a

reduction through a singular perturbation c alculation. 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.

Related Functions

balance(), balmoore(), redschur(), mreduce()

AA11 A12

A21 A22

=BB1

=CC1C2