•** >>[u,s,v]=vsvd(Gf**); % SVD at each frequency;

w**
>>vplot(‘liv,lm’,s), grid** %plot both singular values and grid;

w**
>>pkvnorm(s) **% find the norm from the frequency response of the singular values.
w The
singular values of G(j *w*) are plotted in Figure
4.4, which gives an estimate of ||G||¥ »32.861. The state-space bisection algorithm described previously leads
to ||G||¥ = 50.25±0.01 and the corresponding MATLAB
command is
w** >>hinfnorm(G,0.0001)** or **linfnorm(G,0.0001**) % relative error £0.0001.
w The preceding
computational results show clearly that the graphical method can lead to a wrong
answer for a lightly damped system if the frequency grid is not
sufficiently dense. Indeed, we would get ||G||¥ » 43.525, 48.286 and 49.737
from the graphical method if 400,800, and 1600 frequency points are
used respectively.