
Controller Redundancy Design for Cyber-Physical Systems 71
−0.2 −0.1 0
(a)
(b)
(c)
0.1 0.2
−0.2
−0.1
0
0.1
0.2
x
2
(k)
x
1
(k)
τ
k
(0, 0.001]
Center
τ
k
(0, 0.121]
Center
τ
k
∈ (0,0.001]
Center
τ
k
∈ (0,0.121]
Center
τ
k
∈ (0,0.001]
Center
τ
k
∈ (0,0.121]
Center
−0.2 −0.1 0 0.1 0.2
−0.2
−0.1
0
0.1
0.2
x
1
(k−1)
x
2
(k−1)
τ
k
(0, 0.001]
Center
τ
k
(0, 0.121]
Center
−0.2 −0.1 0 0.1 0.2
−0.2
−0.1
0
0.1
0.2
x
2
(k)
x
1
(k−1)
τ
k
(0, 0.001]
Center
τ
k
(0, 0.121]
Center
FIGURE 3.4 Illustration of MSRs under different network delays (a) projected on x
1
(k) −x
2
(k); (b) projected
on x
1
(k − 1) − x
2
(k − 1); and (c) projected on x
1
(k − 1) − x
2
(k).
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
5
5.2
5.4
5.6
5.8
× 10
−7
Delay (s)
Stability index
FIGURE ...