
Volatility of System Instantaneous Availability ◾ 145
According to Lemma 2, for any norm
and a norm
, there is certainly a
constant C
M
> 0, which makes ⋅≤ ⋅
α
C
M
, set up for all x ∈ V, then
−≤ −≤ −
∗∗
α
αα
∗
rk rCrk rCPA
MM
k
() () (0) .
According to Definition 6.6, the system parameter r(k) is asymptotically stable.
Further, suppose matrix A’s n linearly independent feature vectors α
1
, α
2
, , α
n
;
the corresponding latent roots of which then are λ
1
, λ
2
, , λ
n
(|λ
1
|≥ |λ
2
|≥..≥ |λ
n
|) and
(λ
i
≠ 1), respectively. Because the feature vectors α
1
, α
2
, , α
n
are linearly indepen-
dent, then there is a set of constants s
1
, s
2
, , s
n
that make
−=α+ α+
∗