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Guo et al. Intell Robot 2023;3(4):596-613 I http://dx.doi.org/10.20517/ir.2023.32 Page 9 of 18

where 1 = − Γ , 2 = − Γ , and ( ) = ( ( ), ( )). Therefore, the event-triggered consensus
e −1 e
e −1 e
protocol in this paper can be written as:

( ) = [ 1 , 2 ] ⊗ × ( ) (28)

According to (6), (7), and (8), Converting system (27) to the form in continuous time gives:

¤ ( ) = ⊗ × ( ) + ⊗ × ( )
(29)
0 0 0
= =
1 2 1 2

where ( ) is defined as

( ) ( ) − ( )
( ) = = (30)
( ) ( ) − ( )

Thus, the proof of consensus in system (1) is transformed into the proof of stability of system (27).

Remark 4. The stability of system (27) implies that the state errors between the UAVs are zero. According to
Definition 1, these two propositions are equivalent.

3.2. Analysis of stability
Now, the main result of this paper can be given as follows.

Theorem 1. Consider system (27) and event-triggered consensus protocol (28), sufficient conditions for the
stability of the system are given as follows:

(31)
e
e
e
( + ) − Γ > 0
2
2
(32)
e
e e
e
e
( + ) − Γ − Ψ ( + )Ψ > 0
2
min ( )
k k≤ k k (33)
¯
max ( )
where
e
e
Ψ = ( − ) (34)

" #
2
− −
e
e
¯
= (35)
− −
e
e