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.
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
w>>hinfnorm(G,0.0001) or linfnorm(G,0.0001)% relative error £0.0001.
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