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Tan et al. Complex Eng Syst 2023;3:6 I http://dx.doi.org/10.20517/ces.2023.10 Page 19 of 23

replace the unknown (ℎ), in which is a parameter to be estimated. If this case exists, we can obtain the
estimation value of parameter by employing the optimization algorithm in [24] .

4. SIMULATION EXAMPLE
This section will give an example to verify the feasibility of the above theoretical results. We consider a
semi-Markovian interconnected system composed of three subsystems, and the relevant parameters are as
follows [23] :
[ ] [ ] [ ] [ ]
0 5 0 5 0 5 0 5
A 11 = , A 12 = , A 21 = , A 22 = ,
−9.81 −1 −0.31 −1 −9.81 −1.4 −0.31 −1.4
[ ] [ ] [ ] [ ]
0 5 0 5 0 0
A 31 = , A 32 = , B 11 = B 12 = , B 21 = B 22 = ,
−9.81 −0.5 −0.31 −0.5 0.5 0.4
[ ] [ ] [ ] [ ] [ ]
0 0 0 0 0 0 0 0 0
B 31 = B 32 = , G 121 = , G 122 = , G 211 = , G 212 = ,
0.33 1 0 1 0 0.8 0 0.8 0
[ ] [ ]
0 0 0 0
G 311 = , G 312 = .
0.5 0 0.5 0
[ ]
The transition probability matrix of system (10) is ? ? , where ”?” represents a completely un-
21 (ℎ) 22 (ℎ)
known transition probability, and 21 (ℎ) ∈ [0.4, 0.7], 22 (ℎ) ∈ [−0.6, −0.3]. The scalars and positive matrix
are chosen as = 0.1, = 0.5, = 0.8, 1 = 2 = 3 = 4 = 1, = 20 and = , respectively. By solv-
ing LMIs in Theorem 2, the weighting matrices in equation (4) are Ω 1 = 0.3844, Ω 2 = 0.3839, Ω 3 = 0.3792,
and the corresponding controller gains are
[
]
]
[
1 = 0.1456 −0.2717 , 2 = −0.2089 −0.3153 ,
11 11
[ ] 2 [ ]
1
= −3.5900 −15.3939 , = −3.6974 −15.8393 ,
12 12
]
]
[
[
1 = 0.1452 −0.2697 , 2 = −0.2548 −0.3342 ,
21 21
[ ] 2 [ ]
1
= −2.6929 −12.1132 , = −2.7779 −12.4794 ,
22 22
[ ] 2 [ ]
1
= 0.2304 −0.2927 , = −0.1659 −0.3184 ,
31 31
[ ] 2 [ ]
1
= −1.9339 −12.7768 , = −1.9851 −13.0934 .
32 32
[ ] T [ ] T [ ] T
The initial conditions are given as 1 (0) = −0.45 0.85 , 2 (0) = 0.5 −0.5 , 3 (0) = −0.95 0.55 .
Figure 2 shows the states response of dynamic METM with M=2. To illustrate the effectiveness of the designed
method, Figure 3 presents the state’s response without control input. Figure 4 plots the control input of the sys-
tems. Figure 5 shows the switching states of the semi-Markovian process. Figure 6 depicts the data-releasing
instants and intervals of dynamic METM with M=2. Figure 7 describes the instants and intervals of memory-
less ETM (the case of M = 1). From Figure 6 and Figure 7, we can see that the event-triggered times for M=2
are significantly less than the case of M=1, which illustrates that the dynamic METM has more advantages in
reducing the number of released signals.
5. CONCLUSION
Inthispaper,adynamicMETMhasbeendrawnforthedecentralizedcontrolofinterconnectedsemi-Markovian
systems with partially accessible TRs. Considering both the dynamic METM and partially accessible TRs, a
new kind of interconnected semi-Markovian system model has been designed. By applying the Lyapunov
function theory and the LMI techniques, some sufficient conditions have been obtained to ensure the pro-
posed system is asymptotical stability. Meanwhile, the controller gain matrices and the parameters of dynamic
METM are also solved simultaneously. Finally, a simulation example has been used to verify the effectiveness