196 AND U-SYNTHESIS △f △ Gp(s) Figure 10.5:Robust Performance vs Robust Stability which gives 4 =1.8612 =&Gpk<,a stabilizing controller K and a closed loop transfer matrix Gp p Gp(s) 0 Now generate thel singular value frequency responses of Gp >w=logsp ace(-3,3,300 >Grf=frsp (Gp,w);Gpf is the frequency response of Gp >[u,s,v]vsvd(Gpf); ≥p lot(a,ms) The singular value frequency responses of Gp are shown in Figure 10.6.To test the robust stability,we need to compute &Gp: >Gp11 sel(Gp:1 p,1 p); >norm_of_Gp11 hinfnorm(Gp11,0.001); which gives &GP=0.933<1.So the system is robustly stable.To check the robust performan e,we shall compute the (Gp(j3))for each frequency with ravoh￾ ￾ AND ￾SYNTHESIS ￾ ￾ f  Gps Figure ￾ Robust Performance vs Robust Stability which gives ￾￾ kGpk a stabilizing controller K and a closed loop transfer matrix Gp       z￾ z e￾ e       Gps            p￾ p d￾ d n￾ n            Gps ￾ Gp￾￾ Gp￾ Gp￾ Gp Now generate the singular value frequency responses of Gp  wlogspace   Gpf frspGp w  Gpf is the frequency response of Gp  u s v vsvdGpf   vplot liv m s The singular value frequency responses of Gp are shown in Figure ￾ To test the robust stability we need to compute kGp￾￾k  Gp selGp        norm of Gp hinfnormGp  which gives kGP ￾￾k   ￾ So the system is robustly stable To check the robust performance we shall compute the ￾P Gpj for each frequency with P ￾  f  C f C