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Page 4 of 23 Tan et al. Complex Eng Syst 2023;3:6 I http://dx.doi.org/10.20517/ces.2023.10

Figure 1. A framework of decentralized control system with METM.

set = {1, 2, · · · , } and the generator is given by
{
( ) + ( ), ≠ ,
{ + = | = } = (2)
1 + ( ) + ( ), = ,
where > 0 and lim ( ) = 0, ( ) > 0, ≠ , denotes the transition rate from mode at time to mode
→0
∑
at time + , and satisfies ( ) = − =1, ≠ ( ) < 0, for each = ∈ . More universal uncertain
transitionratesaretakenintoaccountwiththefollowingcases. (1) ( ) iscompletelyunknown; (2) ( ) is
not completely known but there are upper and lower bounds. In case (2), we assume that ( ) ∈ [ , ],

inwhich and areknownrealconstantsmeaningthelowerandupperboundsof ( ) respectively. The

parameter matrix of the system (1) can be abbreviated as (A , G , B ). The TRs matrix can be described
as

 11 ( ) ? 13 ( ) · · · ? 
 
 ? ? 23 ( ) · · · 2 ( ) 
 
 . . . . . . . . . . 
 . . . . . 
 
 ? 2 ( ) ? · · · 
 ( ) 
where ”?” represents a completely unknown element of TRs. For brevity, ∀ ∈ , let ∧ = ∧ , ∪ ∧ , ,
where ∧ , = { : ( ) known upper and lower bounds for ∈ }, ∧ , = { : ( ) completely unknown for
∈ }.

2.2. Interconnected semi-Markovian jump systems with dynamic METM
To economize network resources and improve data transmission efficiency, here one introduces a dynamic
METM. Unlike the other ETM, which only uses instantaneous system information, the proposed METM con-
siders the historically triggered information. Suppose the event-triggered time of the current sampling data
is ℎ, where ( = 1, 2, 3, · · · ) and ℎ represent some positive integers satisfying ⊂ {0, 1, 2, · · · } and the
sampling period of the sensor, respectively. Define the difference between the latest released sampling data
and the current sampling data

Δ ( ) ( ) = ( − +1 ℎ) − ( ℎ + ℎ), = 1, 2, · · · , , (3)

where ∈ 1 = {1, 2, · · · }, denotes the memory length, and ℎ indicates the event-triggered instant. The
next releasing instant +1 ℎ is determined as follows

∑
( ) T ( ) T (4)
+1 ℎ = ℎ + min{ ℎ| (Δ ( )) Ω Δ ( ) > ( ) ( ℎ + ℎ)Ω ( ℎ + ℎ)},

∈ 1
=1