Specifications

norm
16-153
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 iscontinuous and has a nonzero feedthrough (that is,nonzero gain at the
frequency ).
Note that
norm(sys) producesthesameresultas
sqrt(trace(covar(sys,1)))
norm(sys,inf)
computes the infinity norm of any type of LTI model sys.This
norm is infiniteif
sys has poles on theimaginary axis in continuoustime, or on
the unit circle in discrete time.
norm(sys,inf,tol) sets the desired relative accuracy on the 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
Compute its infinity norm by typing
[ninf,fpeak] = norm(H,inf)
Hz
()
∞
max
σ
max
He
j
θ
()()
=
θ
0
π,[]∈
H
2
ω∞
=
Hz
()
z
3
2.841z
2
– 2.875z 1.004–+
z
3
2.417z
2
– 2.003z 0.5488–+
---------------------------------------------------------------------------------
=
H
2