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Page 240 Yang et al. Intell Robot 2022;2(3):223­43 I http://dx.doi.org/10.20517/ir.2022.19

0.18 1.4
0.16
1.2
10 -3
0.14 12
1 0.8 0.035
The norm square of consensus error 0.08 0.1 6 4 2 0 The norm square of consensus error 0.6 0.4 0.015
10
0.12
8
0.025
0.005
0.06
0.04
0.02 -2 25 30 35 40 45 0.2 -0.005 25 30 35 40 45
0
0
-0.02 -0.2
0 10 20 30 40 50 60 0 10 20 30 40 50 60
Time(s) Time(s)
0.4 0.4
0.35 0.35
0.3 0.025 0.25 0.3 0.032
The norm square of consensus error 0.15 0.2 0.015 The norm square of consensus error 0.15 0.2 0.018
0.25
0.025
0.011
0.005
0.004
0.05 0.1 -0.005 25 30 35 40 45 0.05 0.1 -0.003 25 30 35 40 45
0 0
-0.05 -0.05
0 10 20 30 40 50 60 0 10 20 30 40 50 60
Time(s) Time(s)
Figure 6. The norm-squared responses of ( ) under two different scenarios.
3.5
3
Topology Jump Mode 2.5 2

1.5
1
0.5
0 2 4 6 8 10 12 14 16 18 20
Time(s)
Figure 7. A possible mode jumping diagram of communication topologies.

possible topology jumping rule.

Then, the relationship between the statistical properties of channel fading and the H ∞ performance of the
system (6) is discussed. We consider three different values for the variance of the channel fading coefficient
variables ( ) and 0 ( ). By solving the conditions in Theorem 2, the value of the minimum ˆ can be cal-
culated and shown in Table 1. Table 1 lists three groups of simulation experiments. Simultaneously change
the variance of one or two or three groups of fading coefficient variables and calculate the minimum perfor-
mance index ˆ of the system. It can be found from Table 1 that the greater the variance of the channel fading
coefficient variables, the greater the H ∞ performance index ˆ of the system. At the same time, comparing the
second experiment in the first group with the first experiment in the third group, as the number of variances
increases, the H ∞ performance index ˆ of the system also increases. This means that the H ∞ performance of
the system will deteriorate as the effect of the fading channel on the transmitted signal or information becomes
greater.