National Instruments 370757C-01 用户手册

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•

If 

A

 has an imaginary eigenvalue at j

ω

0

, 

linfnorm( )

 returns:

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 

linfnorm( )

 function

then calls itself to solve the continuous-time 

problem, and finally converts the solution back to discrete-time.

Sys=system([-0.2,-1;1,0],[1,0]',[0,1],0);

[sigma,omega]=linfnorm(Sys)

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