September 2013
Intermediate to advanced
398 pages
14h 22m
English
Content preview from Cyber-Physical Systems
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Cyber-Physical System Security—Smart Grid Example ◾ 131
after the Kron-reduced model (Equation 10.5) and let K be a k-dimensional attack set. Permit
VQ
K
T
K
T
T
pp
∈
×
R
to be an orthonormal matrix so that
VDQD
KK
KK
==
BasisIm( BasisIm(
[[
)]
)]
⊥
and let
BBVD BBIDD
ZKKK KK
KK
==
−
()
()
††
Identify the subspace
S
n
*
⊆ R
2
to be the smallest
ABVD VCKerQ C
KKKK K
−
()
() ()
†
,
-condi-
tioned invariant subspace containing Im
()B
K
and allow J
K
to be an output injection matrix so that
()
()
†
ABVD VC JQCS S
KKKK KK
−+
⊆
**
Permit P
K
to be an orthonormal projection matrix onto the quotient space
R
2n
S\
*
, and let
APAB VC JQCPVD
KK KKKK K
T
KK
=− +((
))
.
†
Last, allow H
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