• >>[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.