National Instruments 370757C-01 ユーザーズマニュアル
Chapter 3
System Evaluation
© National Instruments Corporation
3-5
•
If
A
has an imaginary eigenvalue at j
ω
0
,
linfnorm( )
returns:
vOMEGA =
SIGMA = Infinity
where
ω
0
is one of the imaginary eigenvalues of
A
.
•
Even if H is unstable,
linfnorm( )
returns its maximum singular
value on the j
ω axis.
For discrete-time systems
linfnorm( )
converts a discrete-time L
∞
norm computation problem to a continuous-time problem using a Cayley
transformation. For example, it maps the unit circle conformally onto the
complex right half plane using a linear fractional transformation. The
transformation. For example, it maps the unit circle conformally onto the
complex right half plane using a linear fractional transformation. The
linfnorm( )
function
then calls itself to solve the continuous-time
problem, and finally converts the solution back to discrete-time.
Example 3-2
Example of linfnorm( )
Sys=system([-0.2,-1;1,0],[1,0]',[0,1],0);
[sigma,omega]=linfnorm(Sys)
sigma (a scalar) = 5.07322
omega (a scalar) = 0.157081
The
linfnorm( )
function will return the L
∞
norm (
sigma
) of the transfer
matrix H(j
ω) described by
Sys
, and
omega
is the vector of frequencies
where it is achieved.
linfnorm( )
computation can be checked by
plotting the singular values of H(j
ω) as a function of ω (Figure 3-2).
sv=svplot(Sys,{fmin=.01, fmax=1.0});
ω
0