User`s guide

norm
11-152
11norm
Purpose Compute LTI model norms
Syntax norm(sys)
norm(sys,2)
norm(sys,inf)
norm(sys,inf,tol)
[ninf,fpeak] = norm(sys)
Description norm computesthe or norm of acontinuous- ordiscrete-time LTI model.
H
2
Norm
The norm of a stable continuous system withtransfer function , is the
root-mean-square of its impulse response, or equivalently
This norm measures the steady-state covariance (or power) of the output
response to unit white noise inputs .
Infinity Norm
The infinity norm is the peak gain of the frequency response, that is,
where denotes the largest singular value of a matrix.
H
2
L
∞
H
2
Hs
()
H
2
1
2π
------
Trace Hjω()
H
Hjω()()ωd
∞–
∞
∫
=
yHw
=
w
H
2
2
Eyt()
T
yt(){},
t∞→
lim= Ewt()wτ()
T
()δtτ–()I=
Hs()
∞
max Hjω()=
ω
(SISO case)
Hs()
∞
max σ
max
Hjω()()=
ω
(MIMO case)
σ
max
.
()