National Instruments 370753C-01 Manual De Usuario

accurate. Given a variable 

Sys

 built from the matrices {A,B,C,D}, the 

modal decomposition 

SysMod

 is built from T

–1

 AT, T

–1

 B, CT, and D, where 

T is the transformation matrix to modal form. If you have complex poles, 
then T

–1

 AT is in block diagonal form. Initial conditions X

0 

also are 

transformed to T

–1

 X

. 

modal( )

 does not accept input systems in transfer-function form, as the 

concept of modes applies only to a state-variable system representation and 
modes and poles are not interchangeable terms. The poles of a transfer 
function always correspond to the system modes (eigenvalues of the system 
A matrix).

SysRed = mreduce(Sys, keep)

The 

mreduce( )

 function computes a reduced-order form of a given 

system by retaining the states indicated within the vector 

keep

. States not 

specified within this vector are eliminated to obtain a lower-order model 

SysRed

.

mreduce( )

 is implemented by partitioning the state vector x into two 

subvectors, x

1

 (states to be retained in the reduction) and x

2

 (states to be 

eliminated in the reduction), so that:

Similarly, the A, B, and C matrices are partitioned according to this state 
partition:

The model reductions differ for the continuous and discrete-time cases 
because the updates for the states being eliminated are handled differently 
in the respective differential and difference equations. In both cases, the 
eliminated states are taken to be constant over time. In the continuous case, 

1

2

=

11

12

21

22

=

1

2

=

1

2

=