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

internal environments. The methods for solving this problem can be summarized as the following two types:
the adaptive event-triggered mechanism and the dynamic event-triggered mechanism (DETM) [28,29] . For in-
stance, the authors in [30] proposed an improved dynamic ETM to handle fault detections and isolation issues.
And the authors in [31] studied the adaptive event-triggered problem of networked interconnected systems. It
should be noted that the majority of triggering conditions are devised based on the diversity between the cur-
rent sampling signal and the latest released packet [32] . In the above DETM methods, when the relative error
between two sampled signals is faint, the current packet is unlikely to be released. Thus, the error message is
not sufficient to reflex all dynamic characteristics. A sensitive DETM should consider more system trends in
order to achieve a good balance between system performance and utilization of communication resources [33] .
For instance, during the transient process, when the system dynamic curve achieves the response peak, the
proportional error among two sampled signals is faint [34] . The DETM is unlikely to deliver the packet. How-
ever, we expect more sampled signals to be delivered in order to curtail the transient process. For this purpose,
we design a weight-based dynamic METM on the base of the existing literature [35,36] . Applying some of the
recently released information to ETM has shown to be effective in improving system performance. Obviously,
thedynamicMETMcanappropriatelyreleasemorepacketsandgetbettercontrolperformanceunderthesame
triggering parameters within a predefined limited time interval [37] . To our knowledge, there are few results on
dynamic memory event-triggered control for the interconnected semi-Markovian jump systems, which is the
second motivation that lead to our current study.

Enlightened by the viewpoints above, this paper focuses on the decentralized control for a dynamic mem-
ory event-triggered interconnected S-MJSs with partially accessible TRs. The main highlights of this paper
are summarized below: (1) a decentralized control model for the S-MJSs with partially accessible transition
rates is constructed, where a weight-based dynamic METM is first developed to reduce the signal communi-
cation burden and save limited broadband resources; (2) construct a semi-Markovian jump mode-depended
Lyapunov-Krasovskii functional, and some sufficient conditions are deduced to guarantee the asymptotic sta-
bility of the considered system. The controller gain matrices and weighting matrices of dynamic METM are
gained in terms of the LMIs technique. Meanwhile, the design scheme proposed is verified via a simulation
example.

The rest of this paper is described as below: Interconnected semi-Markovian jump system models with mem-
ory event-triggered mechanisms are established in Section 2. Some main results are presented in Section 3. A
simulation example is given in Section 4, and a concise conclusion is drawn in Section 5.

Notation: In this paper, R and R × represent the n-dimensional Euclidean space and the set of × real
T −1
matrix respectively; the superscripts and stand for transposition and inverse, respectively; {· · · }
indicates a block diagonal matrix; > 0(≥ 0) denotes a positive matrix; E{ } submits the mathematical
expectation of the stochastic variable ; the notation ” ∗ ” stands for the symmetric structure.

2. PROBLEM STATEMENT
2.1. System model description
Consider an interconnected semi-Markovian system, which is defined in a fixed probability space ( , , )
andcomposedof subsystems ( = 1, 2, · · · , ). Thedynamicdescriptionofthe thsubsystemisasfollows

∑
¤ ( ) = A ( ) ( ) + B ( ) ( ) + G ( ) ( ), (1)
=1, ≠
where ( ) ∈ R and ( ) represent the state vector of the th subsystem and control input, respectively. The

matrices A ( ), B ( ) are of proper dimensions. G ( ) denotes the interconnection matrix of the th and
th subsystems; { ≥ 0} defines a continuous time semi-Markovian process taking discrete values in a finite