Corrections: Essentials of robust control Errors listed here appeared in the first printing. Most of those errors have bee orrected in the recent printing except those with *k Convention: Page aa is denoted as Prr. Line aca from the top of the page is denoted as Lrrr while line ar from the bottom of the page is denoted as -lrt. 1. Pviii, L5, itp ee. lsu. edu should be ftp gate. ee. lsu. edu 2. P20, Ll, B=U1AU1 should be B=UiAVi 3. P38 -L9. at lease should be at least 4. P42, -L6, left-unit eigenvectors should be left-unit eigenvectors such that yci= 5. P43, problem 3.7, G3 shor G1, G should be 6. * P62, problem 4.3, T should be TI. 7. P77, L2 and L3, L= -lqr(A', C, eye(n),eye(p))and L=-place(A', C, Pl) hould be l lqr(a', C, eye(n), eye(p))and L=-place(a', c, Pl)'(i.e 8.P101.L12 S(s)lks=‖BF1(s)S(s)、≥|Bz2(2)S(2)=|B1(2) should be S(s)l=‖B=1(s)S(s)l≥|B2(x)S(2) (The last equality holds only when z is a right half plane zero of L) 9. P102, Problem 6.4, Design a controller should be design a lead or lag controller 10. P102. Problem 6.6 should be restated as: Let P (1-s)(s+2) Design a lead or lag controller so that the system has at least 30 phase margin with loop gain 22 for any frequency w < 0. 1 and the smallest possible bandwidth(or crossover frequency) 11.**P114,L13-15,C2{-∞,0) should be L2(-∞,0 be reAi(A1)≤0. 3. * P138, -L10, MGwo)=UGjwzGjwoV* Gwo)should be MGwo=UGwo2(wo) Gwo) 15. P158, Figure 8.20 should be partially filled
1 Corrections: Essentials of Robust Control Errors listed here appeared in the first printing. Most of those errors have been corrected in the recent printing except those with ∗∗. Convention: Page xx is denoted as P xx. Line xxx from the top of the page is denoted as Lxxx while line xx from the bottom of the page is denoted as −Lxx. 1. Pviii, L5, ftp ee.lsu.edu should be ftp gate.ee.lsu.edu 2. P20, L1, B = U∗ 1 AU1 should be B = U∗ 1 AV1. 3. P38, -L9, at lease should be at least. 4. P42, -L6, left-unit eigenvectors should be left-unit eigenvectors such that y∗ i xi = 1. 5. P43, problem 3.7, G3 should be G1, G should be G3. 6. ∗∗ P62, problem 4.3, π should be πI. 7. P77, L2 and L3, L = −lqr(A0 , C0 , eye(n), eye(p)) and L = −place(A0 , C0 ,Pl) should be L = −lqr(A0 , C0 , eye(n), eye(p))0 and L = −place(A0 , C0 ,Pl)0 (i.e., transposed). 8. P101, L12, kS(s)k∞ = B−1 p (s)S(s) ∞ ≥ |B−1 p (z)S(z)| = |B−1 p (z)| should be kS(s)k∞ = B−1 p (s)S(s) ∞ ≥ |B−1 p (z)S(z)| (The last equality holds only when z is a right half plane zero of L.) 9. P102, Problem 6.4, Design a controller should be design a lead or lag controller. 10. P102, Problem 6.6 should be restated as: Let P = 5 (1 − s)(s + 2). Design a lead or lag controller so that the system has at least 30o phase margin with loop gain ≥ 2 for any frequency ω ≤ 0.1 and the smallest possible bandwidth (or crossover frequency). 11. ∗∗ P114, L13-15, L2[−∞, 0) should be L2(−∞, 0]. 12. ∗∗ P117, -L6, λi(A11) ≤ 0 should be Reλi(A11) ≤ 0. 13. ∗∗ P138, -L10, M(jw0) = U(jw)Σ(jw0)V ∗(jw0) should be M(jw0) = U(jw0)Σ(jw0)V ∗(jw0). 14. P155, -L3, y1 should be y2. 15. P158, Figure 8.20 should be partially filled
0 Figure 0. 1: Stability region for a=5 17. P163, Problem 8. 17, smallest should be larges 18. P180,-L4, starp(P, K, dimy, dimu) should be starp(P, K) 19.P199,-L6, →H△(a0(M1M2 1((M,△2)) (M) M21 M22 111/a M12/a 22
2 −2 −1.5 −1 −0.5 0 0.5 1 1.5 −2 −1.5 −1 −0.5 0 0.5 1 1.5 Figure 0.1: Stability region for a = 5 16. ∗∗ P161, L1, N = 2(s+1) (s+2)2 should be N = s+1 (s+2)2 17. P163,,Problem 8.17, smallest should be largest. 18. P180, -L4, starp(P, K, dimy, dimu) should be starp(P, K). 19. P199, -L6, ⇐⇒ µ∆(M) M11/α M12/α M21 M22 = 1. Hence max ∆2∈B∆2 µ1 (F` (M, ∆2)) = α : µ∆(M) M11/α M12/α M21 M22 = 1 . should be ⇐⇒ µ∆ M11/α M12/α M21 M22 = 1. Hence max ∆2∈B∆2 µ1 (F` (M, ∆2)) = α : µ∆ M11/α M12/α M21 M22 = 1
A/a b/a hould be 21.77 21. P238, L12, follows immediately form. should be follows immediately from 22. * P239, L4, The equivalence between (ii) and (iv)is obvious should be The equivalence between(iii) and (iv)is obvious by noting the fact that A+Br-Id'C able if|G‖<7 23. P239, L13, XBR-ID"C)should be XBR-D"C 24.P254,L1l,att→ oo should be as t→c P268, Problems 13.4 and 13.6, P=10(s+2)/s(s+1 )should be P= 10(s 2)/(s+1) 26.P301, Problem147,P=10(s+2)/s(s+1)2 should be p=10(s+2)/(s+1) 7.P377 12,‖(z) should be‖(2) 29.P382,L10,PR(M△)=∞ should be pr(M△)=0 30.P383,L3,“ Since d is nonsingular and d*D=D2∈D” should be“ Since d is nonsingular and D"D∈D” 31.P383,L17,“ note that o=Q* and Q"G=QG=GQ” should be“ note that G=QG=GQ
3 20. P200, L2 αmax = α : µ∆(M) A/α B/α C D = 1 = 21.77. should be αmax = α : µ∆ A/α B/α C D = 1 = 21.77. 21. P238, L12, follows immediately form .. should be follows immediately from ... 22. ∗∗ P239, L4, The equivalence between (ii) and (iv) is obvious should be The equivalence between (iii) and (iv) is obvious by noting the fact that A+BR−1D∗C is stable if kGk∞ < γ. 23. P239, L13, XBR−1D∗C) should be XBR−1D∗C. 24. P254, L11, at t → ∞ should be as t → ∞. 25. P268, Problems 13.4 and 13.6, P = 10(s + 2)/s(s + 1)2 should be P = 10(s + 2)/(s + 1)3. 26. P301, Problem 14.7, P = 10(s + 2)/s(s + 1)2 should be P = 10(s + 2)/(s + 1)3. 27. P377, - 12, k∆(z)k should be k∆(z)k∞. 28. P377 -L6, (u0, u1,...,ul−1) should be u = (u0, u1,...,ul−1) 29. P382, L10, ρR(M∆) = ∞ should be ρR(M∆) = 0. 30. P383, L3, “Since D is nonsingular and D∗D = D2 ∈ D” should be “Since D is nonsingular and D∗D ∈ D”. 31. P383, L17, “note that Q = Q∗ and Q∗G = QG = GQ” should be “note that Q∗G = QG = GQ