Page 64 - Read Online

Page 2 of 23 Tan et al. Complex Eng Syst 2023;3:6 I http://dx.doi.org/10.20517/ces.2023.10

1. INTRODUCTION
With the prompt development of modern industry, the requirements for system scale and control objectives
are increasing. Many single systems improve their own characteristics through interconnection to meet local
[1]
and global performance requirements . Nowadays, interconnected systems are widely used in actual pro-
[3]
[2]
duction and life, such as power systems , intelligent transportation systems , and network communication
[4]
systems . The interconnected systems are large-scale composite systems which are composed of several sub-
systems connected in a specific way. Interconnected systems usually have strong coupling, strong uncertainty,
high dimensions, and other characteristics. Thus, the existing traditional control strategies designed for a
single system are difficult to directly solve the analysis and control problems of interconnected systems [5,6] .
Therefore, many scholars are devoted to the control analysis and design for this kind of large-scale system.

Recently, decentralized control methods have been applied to interconnected control systems, where the sub-
system only uses its own information to achieve the control design. Due to its simple structure, low cost, and
high reliability, the decentralized control method has drawn wide attention in the control design of large-scale
complex systems, and numerous research results have emerged [7,8] . For example, a decentralized control strat-
[9]
egyforthelinearizedpowersystemwithdifferentloaddistributionswasstudiedin . Adecentralizedadaptive
sliding mode control mechanism for the stability of large-scale semi-Markovian jump interconnected systems
was proposed in [10,11] , and a decentralized output feedback control for large-scale systems with communica-
tion delay and random shortcoming measurements was studied in [12] . Recently, it has also witnessed rapid
growth in the application of decentralized control methodologies in the field of engineering. For instance, a
decentralized Markovian jump ∞ control routing strategy for mobile multi-agent networked systems were
investigated in [13] . The adaptive fuzzy decentralized tracking control for large-scale interconnected nonlinear
networked control systems was studied in [14,15] , and a Lyapunov-function based event-triggered control was
adopted to develop nonlinear discrete-time cyber-physical systems [16] . However, the decentralized control of
interconnected systems is still an open field to be developed, and there are still many problems to be discussed.

It is noticed that most actual systems are often affected by some sudden changes during operation, and such
systems can be represented by Markovian jump systems (MJSs). However, the residence time in MJSs fol-
lows exponential distribution and the distribution of residence time has no memory, that is, the transition
rate is a random process independent of past modes, which brings some limitations to its application [17] . In
comparison with MJSs, the dwell time of semi-Markovian jump systems (S-MJSs) can obey non-exponential
distributions, such as Weibull distribution and Gaussian distribution. The S-MJSs release the limitation of the
probability distribution function and reduce the conservatism of the system, thus they have wider application
in practice [18] . In recent years, many important theoretical advances and practical significance for S-MJSs can
be found. For example, the authors in [19] studied the dynamic output feedback control for a class of linear
S-MJSs in the discrete-time domain. The stability of singular switching S-MJSs with uncertain TRs was de-
veloped in [20] . In [21] , by using the LMI method, the authors studied the stochastic stability of linear S-MJSs,
where TRs were divided into different parts. It is often difficult to fully know the jumping probability of modes
when the system is modeled as a MJS or S-MJS. It is noticed that the TRs in S-MJSs are more complex because
they stick to a more ordinary distribution instead of an exponential distribution [22,23] . Consequently, the
study of different forms of TRs would increase the complexity of the process of control design. Recently, an
estimation method has been proposed for nonlinear S-MJSs with partially unknown transition probability and
output quantization, see [24] and the literature wherein. However, few related works involve exactly unknown
and uncertain bounded transition rates of interconnected S-MJSs, which is one of the main motivations of this
paper.

Additionally, the event-triggered mechanism (ETM) was drawn to avoid the waste of network resources. Com-
pared with the periodic sampling method, the ETM can avoid the generation of data redundancy [25–27] . How-
ever, if the event-triggered threshold argument is a constant, it is difficult to fit in the variety of outside and