User`s guide

norm
11-153
The discret e-time counterpart is
Usage norm(sys) or norm(sys,2) both return the norm of the TF, SS, or ZPK
model
sys. This norm is infinite in the following cases:
•
sys is unstable.
•
sys is continuousand has anonzero feedthrough (that is, nonzero gain atthe
frequency ).
Note that
norm(sys) produces the same result as
sqrt(trace(covar(sys,1)))
norm(sys,inf)
computes the infinity norm of any type of LTI model sys.This
norm is infinite if
sys has poles on the imaginary axis in continuous time, or on
the unit circle in d iscrete time.
norm(sys,inf,tol) sets the desired relative accuracy on t he computed
infinity norm (the default value is
tol=1e–2).
[ninf,fpeak] = norm(sys,inf) also returns the frequency fpeak where the
gain achieves its peak value.
Example Consider the discrete-time transfer function
with sample time 0.1 second. Compute its norm by typing
H = tf([1 –2.841 2.875 –1.004],[1 –2.417 2.003 –0.5488],0.1)
norm(H)
ans =
1.2438
Hz()
∞
max σ
max
He
jθ
()()=
θ0π,[]∈
H
2
ω∞=
Hz()
z
3
2.841z
2
– 2.875z 1.004–+
z
3
2.417z
2
– 2.003z 0.5488–+
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H
2