January 2016
Intermediate to advanced
300 pages
6h 54m
English
book
Fluctuation Mechanism and Control on System Instantaneous Availability
by Yi Yang, Yong-Li Yu, Li-Chao Wang
Content preview from Fluctuation Mechanism and Control on System Instantaneous Availability
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86 ◾ System Instantaneous Availability
eorem 5.5: Matrix B has the characteristic root γ = 1, which is a simple root.
If X
0
= (x
1
, x
2
, …, x
2n+2
)
T
stands for the feature vector of γ = 1 on C, the value of
X
0
is unique and satisfies
==
+
xx
D
n
1
12
1
∏
()
=−λ
=+
=
−
…
1
1,2,3,
,1
0
2
1
x
D
ji n
i
j
i
∏
()
=−µ
=+
++
=
−
…
1
1,2,3,
,1
1
0
2
2
1
x
D
ji n
ni
j
i
.
In the formula,
∏
∑
∏
∑
() ()
=+ −λ
+−
µ
=
−
=
+
=
−
=
+
Djj
j
i
i
n
j
i
i
n
21 1
0
2
2
1
0
2
2
1
12
.
Prove: According to eorem 5.4, γ = 1 is the simple characteristic root of
matrix B, which is equivalent to
−γ
γ
≠
γ=
dB I
d
0
1
. (5.6)
en, Formula 5.6 is proven:
−γ
γ
γ=
dB I
d
1
() () ()
()
()
() ()
()
()
()
=
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