IEEE Systems, Man and Cybernetics Magazine - July 2022 - 45

Theorem 2
Under Assumption (),AM
limE ml
t 3
"
for given positive scalars z and
h , system (7) can achieve exponential consensus with
convergence rate a and an ADT satisfying
xxa2 ) =
a
lna k
1
()b
ml
1
max
Proof
It follows from Theorem 1 that we have
js # 11 l
b
(, ()) ^^mmax
l
tt
# Eb
mj s
+- m
(( )) (, ()).
E
d
h
-
Here, we take (( ) (( ))).
Y=+ -
11 ttl
max tt tt
d
mmax
js # mj s
lnY
tt et tt t
-
x ()E (( )) (, ()).
l
a tt0
-
b
b
max 00 0
E mmax
b
Equation (25) can be rewritten as
(, ())
- 0
b
(26)
It follows from the Mittag-Leffler expansion function
(see [16]) that we obtain
10
-15
-10
-5
5
2
4 68 10
t (s)
(a)
10
5
-5
-10
20
t (s)
(b)
12
22
32
42
10
5
-5
-10
510155 10
t (s)
(c)
Figure 2. The consensus error ps for each agent p of system (32) with input up (4), p ,, ,.12 34=
consensus error p1s for each agent p of system (32) with input up (4). (b) The consensus error p2
agent p of system (32) with input up (4). (c) The consensus error p3
input up (4).
(a) The
s for each
s for each agent p of system (32) with
July 2022 IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE 45
15
20
13
23
33
43
12
14
16
18
b ^
00 0
max ^tt b
- h hh
tt0
a
x
-
(25)
Y .
(24)
js # b
b (( ))tt lim e1 () ()bm -b tt0
1
max
- 0
# t " 3 b
max
l
.
From (26) and (27), we obtain
(, ())( ,( )),
tt et t
1 ()
a jstt0
00
where
the convergence rate =+Y_ln
Denot i ng {j tt {( ( ))} and
ax 10 .
a ^h i
1 b
ml
can get
{s ## (29)
() (, ())and (, ())( ).
tt tt tt0
js js hs
00
From (28) and (29), we have
() ()
-
0 {h b , p 12
max
== we
minmax {( ( ))},
sh js
(27)
(28)
11 # 11a -
p tt Met t
tt
0 00 00
()
whereMN , , ...,==1.
p()
() ,
-
as t " 3 Since the
convergence rate a1 0 , we conclude that system (7) can
reach exponential consensus with the ADT satisfying (24).
11
21
31
41
20
p2(t )
p1(t )
p3(t )

IEEE Systems, Man and Cybernetics Magazine - July 2022

Table of Contents for the Digital Edition of IEEE Systems, Man and Cybernetics Magazine - July 2022

Contents
IEEE Systems, Man and Cybernetics Magazine - July 2022 - Cover1
IEEE Systems, Man and Cybernetics Magazine - July 2022 - Cover2
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 1
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 2
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 3
IEEE Systems, Man and Cybernetics Magazine - July 2022 - Contents
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 5
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 6
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 7
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 8
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 9
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 10
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 11
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 12
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 13
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 14
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 15
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 16
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 17
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 18
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 19
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 20
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 21
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 22
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 23
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 24
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 25
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 26
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 27
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 28
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 29
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 30
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 31
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 32
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 33
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 34
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 35
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 36
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 37
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 38
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 39
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 40
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 41
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 42
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 43
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 44
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 45
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 46
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 47
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 48
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 49
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 50
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 51
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 52
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 53
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 54
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 55
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 56
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 57
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 58
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 59
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 60
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 61
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 62
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 63
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 64
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 65
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 66
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 67
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 68
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 69
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 70
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 71
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 72
IEEE Systems, Man and Cybernetics Magazine - July 2022 - 73
IEEE Systems, Man and Cybernetics Magazine - July 2022 - Cover3
IEEE Systems, Man and Cybernetics Magazine - July 2022 - Cover4
https://www.nxtbook.com/nxtbooks/ieee/smc_202310
https://www.nxtbook.com/nxtbooks/ieee/smc_202307
https://www.nxtbook.com/nxtbooks/ieee/smc_202304
https://www.nxtbook.com/nxtbooks/ieee/smc_202301
https://www.nxtbook.com/nxtbooks/ieee/smc_202210
https://www.nxtbook.com/nxtbooks/ieee/smc_202207
https://www.nxtbook.com/nxtbooks/ieee/smc_202204
https://www.nxtbook.com/nxtbooks/ieee/smc_202201
https://www.nxtbook.com/nxtbooks/ieee/smc_202110
https://www.nxtbook.com/nxtbooks/ieee/smc_202107
https://www.nxtbook.com/nxtbooks/ieee/smc_202104
https://www.nxtbook.com/nxtbooks/ieee/smc_202101
https://www.nxtbook.com/nxtbooks/ieee/smc_202010
https://www.nxtbook.com/nxtbooks/ieee/smc_202007
https://www.nxtbook.com/nxtbooks/ieee/smc_202004
https://www.nxtbook.com/nxtbooks/ieee/smc_202001
https://www.nxtbook.com/nxtbooks/ieee/smc_201910
https://www.nxtbook.com/nxtbooks/ieee/smc_201907
https://www.nxtbook.com/nxtbooks/ieee/smc_201904
https://www.nxtbook.com/nxtbooks/ieee/smc_201901
https://www.nxtbook.com/nxtbooks/ieee/smc_201810
https://www.nxtbook.com/nxtbooks/ieee/smc_201807
https://www.nxtbook.com/nxtbooks/ieee/smc_201804
https://www.nxtbook.com/nxtbooks/ieee/smc_201801
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_1017
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0717
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0417
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0117
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_1016
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0716
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0416
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0116
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_1015
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0715
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0415
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0115
https://www.nxtbookmedia.com