Norm of linear model
n = norm(sys)
n =
norm(sys,2)
n = norm(sys,inf)
[n,fpeak]
= norm(sys,inf)
[...] = norm(sys,inf,tol)
or n
= norm(sys
)
return the H_{2} norm of
the linear dynamic system model n
=
norm(sys
,2)sys
.
returns
the H_{∞} norm of n
= norm(sys
,inf)sys
.
[
also returns the frequency n
,fpeak
]
= norm(sys
,inf)fpeak
at
which the gain reaches its peak value.
[...] = norm(
sets
the relative accuracy of the H_{∞} norm
to sys
,inf,tol
)tol
.
This command requires Control System Toolbox™ license.

Continuous or discretetime linear dynamic system model. 

Positive real value setting the relative accuracy of the H_{∞} norm. Default: 0.01 

H_{2} norm or H_{∞} norm of
the linear model If 

Frequency at which the peak gain of 
This example uses norm
to compute the H_{2} and H_{∞} norms
of a discretetime linear system.
Consider the discretetime transfer function
$$H(z)=\frac{{z}^{3}2.841{z}^{2}+2.875z1.004}{{z}^{3}2.417{z}^{2}+2.003z0.5488}$$
with sample time 0.1 second.
To compute the H_{2} norm of this transfer function, enter:
H = tf([1 2.841 2.875 1.004],[1 2.417 2.003 0.5488],0.1) norm(H)
These commands return the result:
ans = 1.2438
To compute the H_{∞} infinity norm, enter:
[ninf,fpeak] = norm(H,inf)
This command returns the result:
ninf = 2.5488 fpeak = 3.0844
You can use a Bode plot of H(z) to confirm these values.
bode(H) grid on;
The gain indeed peaks at approximately 3 rad/sec. To find the peak gain in dB, enter:
20*log10(ninf)
This command produces the following result:
ans = 8.1268
norm
first converts sys
to
a state space model.
norm
uses the same algorithm as covar
for the H_{2} norm.
For the H_{∞} norm, norm
uses
the algorithm of [1]. norm
computes
the H_{∞} norm (peak
gain) using the SLICOT library. For more information about the SLICOT
library, see http://slicot.org.
[1] Bruisma, N.A. and M. Steinbuch, "A Fast Algorithm to Compute the H_{∞}Norm of a Transfer Function Matrix," System Control Letters, 14 (1990), pp. 287293.