National Instruments 370757C-01 用户手册
Chapter 3
System Evaluation
3-4
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factor by which the RMS value of a signal flowing through H can be
increased.
increased.
By comparison, the H
2
norm is defined as:
This norm can be interpreted as the RMS value of the output when the input
is unit intensity white noise. It can be computed in Xmath using the
is unit intensity white noise. It can be computed in Xmath using the
rms( )
function.
For discrete-time systems with a stable H,
where is the maximum singular value and H(e
j
ω
) is the transfer matrix
under consideration.
linfnorm( )
[sigma, vOMEGA] = linfnorm( Sys, {tol,maxiter} )
The
linfnorm( )
function computes the L
∞
norm of a dynamic system
using a quadratically convergent algorithm. The
linfnorm( )
function
relies on eigenvalue calculations of a Hamiltonian matrix with twice as
many states as
many states as
Sys
and, consequently, may be unreliable for large systems.
A singular value plot created with
svplot( )
can be used as an alternative
in these cases. Refer to the
•
The keyword
tol
controls the required relative accuracy. The default
is 0.01.
maxiter
is the maximum number of iterations. The default
is 15.
•
If the maximum norm is found at
ω = ∞,
linfnorm( )
returns:
vOMEGA = Infinity
sigma = gain at infinity.
H
2
1
2
π
------
σ
i
H j
ω
( )
(
)
2
i
1
=
k
∑
∞
–
∞
∫
=
dw
H
∞
max
ω
π π
,
–
(
)
∈
σ H e
j
ω
(
)
(
)
=
σ