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nel fading of single systems [22–26] , channel fading for multi-agent systems [27–29] . The reference [22] designed
a nonparallel distribution compensation interval type-2 fuzzy controller to address dynamic event-triggered
control problems for interval type-2 fuzzy systems subject to fading channel, where the fading phenomenon
is characterized by a time-varying random process. The literature [23] focused on the finite-horizon ∞ state
estimation problem of periodic neural networks subject to multi-fading channels. By employing the stochastic
analysis method and introducing a set of correlated random variables, sufficient criteria to ensure the stochas-
tic stability of the estimation error system with correlated fading channels were obtained and the desired ∞
performance was achieved. In [25] , the event-triggered asynchronous guaranteed that cost control problem for
Markov jump neural networks subject to fading channels could be addressed, where a novel rice fading model
was established to consider the effects of signal reflections and shadows in wireless networks. The consensus
tracking problem of second-order multi-agent systems with channel fading was investigated using the sliding
mode control method, and the feasible distributed sliding mode controller was designed by introducing the
statistical information of channel fading to the measure functions of the consensus errors [27] . It should be
pointed out that most of the literatures mentioned above on channel fading in multi-agent systems only con-
sider the fading effect among the follower agents and ignore the fading effect between the leader agent and
the follower agents. As stated earlier, the leader plays a crucial role in the leader-following consensus problem.
To improve the applicability of the controller and the ability to deal with the problem, it is reasonable and
necessary to consider both the fading effect of leader-to-follower and follower-to-follower agents at the same
time in the channel fading problem of multi-agent systems. This is one of the motivations of this paper.

On the other hand, the communication topology of multi-agent systems may change in practice due to various
factors, such as sudden changes in the environment, communication range limitations, link failures, packet
loss, malicious cyber attacks, etc. Given this, many researchers assume that the topology among agents is
time-varying or Markov switching. Some good consensus results for multi-agent systems under time-varying
topology and Markov switching topology have been reported in the past decade [30–34] . For example, the
work [33] investigated the coupled group consensus problem for general linear time-invariant multi-agent sys-
tems under continuous-time homogeneous Markov switching topology. The designed linear consensus pro-
tocol can achieve coupled group consensus of the considered system under some algebraic and topological
conditions. It is worth noting that since the transition probability in Markov jump process is constant and
there is no memory characteristic, there are still some limitations in using Markov jump process to model
topology switching among agents. Recently, a class of more general semi-Markov jump processes with a non-
exponential distribution of sojourn-time (the time interval between two consecutive jumps) and time-varying
transition probabilities has attracted interest of many scholars and has been used to characterize the topo-
logical switching among agents [35–38] . For example, the leader-following consensus of a multi-agent system
underasampled-data-basedevent-triggeredtransmissionschemewasrealized [35] ,whereasemi-Markovjump
process was employed to model the switching of the network topologies. The containment control problem
concerning semi-Markov jump multi-agent systems with semi-Markov switching topologies was studied by
designing static and dynamic containment controllers [37] . Under a semi-Markov switching topology with par-
tially unknown transition rates, the ∞ leader-follower consensus control of a class of nonlinear multi-agent
systems with external perturbations was achieved, and sufficient conditions for ensuring system consistency
and ∞ performance were derived based on the linear matrix inequality form [38] . However, most of the above
literature on semi-Markov switching topology is considered for the continuous system case. As a matter of
fact, in the discrete-time case, the semi-Markov jump process can exert a stronger modeling ability and have
a larger application range. The reason is that the probability density function of sojourn-time in the discrete
semi-Markov jump process can be of different types in different modes, or of the same type but with different
parameters. In order to make the modeling of switching topology more realistic, it is very necessary and valu-
able to employ discrete-time semi-Markov switching topologies. Naturally, how to deal with the consensus
problem of multi-agent systems in this situation is a key point. Recently, the discrete semi-Markov jump pro-
cess was adopted to model general linear systems and a semi-Markov kernel method was proposed to address