Fall 2001 163119-7 ssues Note that it is actually not easy to find gmax directly using the state space techniques It is easy to check if Gmax < r So we just keep changing y to find the smallest value for which we can show that Gmax y(called ?min Bisection search algorithm Bisection search algorithm(see web 1. Select y, O so that≤Gmax≤mu 2. Test (u -nu/y< TOL Yes→Stop(Gmnk≈(7n+) No→g o to step 3 3. With y=5(n +Yu), test if Gmax y using Ai(H) 4. If Ai H)E jR, then set y(test value too low), otherwise set fu=y and go to step 2 This is the basis of Hoo control theoryFall 2001 16.31 19–7 Issues • Note that it is actually not easy to find Gmax directly using the state space techniques – It is easy to check if Gmax < γ – So we just keep changing γ to find the smallest value for which we can show that Gmax < γ (called γmin) ⇒ Bisection search algorithm. • Bisection search algorithm (see web) 1. Select γu, γl so that γl ≤ Gmax ≤ γu 2. Test (γu − γl)/γl < TOL. Yes ⇒ Stop (Gmax ≈ 1 2(γu + γl)) No ⇒ go to step 3. 3. With γ = 1 2(γl + γu), test if Gmax < γ using λi(H) 4. If λi(H) ∈ jR, then set γl = γ (test value too low), otherwise set γu = γ and go to step 2. • This is the basis of H∞ control theory