Specifications

norm
16-152
16norm
Purpose Compute LTI model norms
Syntax norm(sys)
norm(sys,2)
norm(sys,inf)
norm(sys,inf,tol)
[ninf,fpeak] = norm(sys)
Description norm computes the or normofacontinuous-ordiscrete-timeLTI model.
H
2
Norm
The norm of a stable continuous system with transfer 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.
The discrete-time counterpart is
H
2
L
∞
H
2
Hs
()
H
2
1
2
π
------
Trace Hj
ω()
H
Hj
ω()()ω
d
∞
–
∞
ò
=
yHw= w
H
2
2
Eyt
()
T
yt
(){}
,
t
∞→
lim= Ewt
()
w
τ()
T
()δ
t
τ
–
()
I=
Hs
()
∞
max Hj
ω()
=
ω
(SISO case)
Hs
()
∞
max
σ
max
Hj
ω()()
=
ω
(MIMO case)
σ
max
.()