>>[u,s,v]=vsvd(Gf); % SVD at each frequency;
>>vplot(‘liv,lm’,s), grid %plot both singular values and grid;
>>pkvnorm(s) % find the norm from the frequency response of the singular values.
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
>>hinfnorm(G,0.0001) or linfnorm(G,0.0001) % relative error £0.0001.
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.