Gioele Zardini Control Systems II FS 2018
Errata of the Script
Notation:
• Red: corrections.
List of Corrections
• On page 77:
The correct formula for Equation 4.7 is
kAkF =kAk2 =
m
X
i=1 n
X
j=1
a2ij
!12
, (1.1)
• On page 78:
The correct formula for Equation 4.14 is
kGkp = sup
kuk6=0
kGuk kuk
, (1.2)
• On page 83:
The correct form of Equation 4.41 is kAk22 = max
kuk=1y∗·y
= max
kuk=1(A·u)∗ ·(A·u)
= max
kuk=1u∗·A∗·A·u
= max
i µ(A∗·A)
= max
i σi2.
(1.3)
• On page 84:
The correct form of Equations 4.49 and 4.50 is
Σ =
σ1 0 . . . 0 . .. ... ... σp 0 . . . 0
∈Rp×m, p < m (1.4)
Σ =
σ1
. ..
σm 0 . . . 0
... ... 0 . . . 0
∈Rp×m, p > m. (1.5)
• On page 98, Equation 4.119:
eψ1·j 0 0 eψ2·j
· ν1
ν2
=
P11(jω) P12(jω) P21(jω) P22(jω)
·
eϕ1·j 0 0 eϕ2·j
· µ1
µ2
. (1.6)
1
Gioele Zardini Control Systems II FS 2018
• On page 109, Equation 4.164 and Definition 9:
P(s) =C(sI−A)−1B+D. (1.7)
• On Equation 4.261 one has
σ(C(jω))≤M¯ (1.8)
• On page 179, equations 6.44 and 6.45 are switched (an the relative definitions).
• On page 215, Equation 8.29:
A|extX∞+X∞Aext+Cext,z| Cext,z +X∞
1
γ2Bext,wBext,w| −Bext,uB|ext,u
X∞ (1.9)
2