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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 5 of 18

(
− ≠
=
= Í
=1
( (3)
− ≠
ℎ = Í
=
=1
The mass matrix of the system is recorded as = ( 1 , 2 , , ) > 0. Describe system (1) by using
matrices as follows:

−1

¥ + −1 ⊗ ¤ + ⊗ = 0 (4)
Remark 3. Actual physical meaning in the formula denoted by is the dimension of state space, which is
usually defined as 3.

Due to the limited refresh rate and sampling frequency of sensors and processors, the event triggering mecha-
nism is proposed to reduce the pressure on sensors and save processor resources while ensuring that they can
still react quickly in the face of unexpected situations.

State error is an important decision factor in event-triggered consensus control. Define ( ) = ( ) − 1 ( )
and ( ) = ( ) − 1 ( ), which denote position error and state error, respectively. Apart from this, define
( ) = ( 2 ( ), , ( )) and ( ) = ( 2 ( ), , ( )), ( ) = ( ( ), ( )). Suppose the incremental time
column that satisfies the event-triggered condition is { 1 , , }. System (1) is equivalent to

¤
( ) = ( )
(5)
¤ ( ) = [ 1 2 ] ⊗ ( ) ∈ [ , +1 )

We define

0
= (6)
1 2

( ) ( ) − ( )
( ) = = (7)
( ) ( ) − ( )

And we have

¤
( ) = ( )
¤ ( ) = [ 1 2 ] ⊗ ( )

( )
= [ 1 2 ] ⊗
( )

( ) + ( )
= [ 1 2 ] ⊗
( ) + ( )

( ) ( )
= [ 1 2 ] ⊗ ( + )
( ) ( )