In this study, the mean square consensus problem for stochastic multi-agent systems with nonlinear protocols is concerned. In particular, the topological structure of the system is characterised by state-dependent directed graph, in which the edges are described by nonlinear function related to the states and possess much better performance than before. A novel proposition based on matrix theory is proposed to conquer the challenges of time-invariant asymmetric matrix. In view of the communication burden and practically, a time-dependent event-triggered strategies are explored, where the control input on each agent is updated only when a certain triggering condition is violated. Then, some sufficient conditions for mean square consensus of stochastic multi-agent with state-dependent topology are established. Furthermore, a positive lower bound for inter-event times can be found such that the Zeno phenomenon is eliminated. Finally, a simulation example is utilised to illustrate the validly of developed theoretical results and the effectiveness of the control protocol.

In this paper, the exponential leader-following consensus problem is investigated for networked multi-agent systems. In order to further reduce the usage of the communication resources, event-triggered delayed impulsive control strategy is put forward, which successfully combines the delayed impulsive control and event-triggered mechanism, and the delayed impulsive controller is implemented only at event-triggered instants. By constructing the novel Lyapunov based event-triggered strategy and impulsive control theory, some easy-to-check conditions are derived such that the error system is exponentially stable. Furthermore, it is shown that the Zeno behavior can be eliminated from the event-triggering rules. Numerical simulation is proposed to illustrate the effectiveness of the theoretical results.

The consensus problem in stochastic multi-agent systems (MASs) with Markovian switching is addressed by proposing a novel distributed dynamic event-triggered (DDET) technique based on periodic sampling to reduce information transmission. Unlike traditional event-triggered control, the proposed periodic sampling-based DDET method is characterized by the following three advantages: (1) The need for continuous monitoring of the event trigger is eliminated. (2) Zeno behavior in stochastic MASs is effectively prevented. (3) Communication costs are significantly reduced. Based on this, sufficient conditions for achieving consensus in the mean-square sense are derived using Lyapunov–Krasovskii functions, providing a solid theoretical foundation for the proposed strategy. The effectiveness of the proposed DDET control is validated through two numerical examples.

To construct Caputo fractional-order time-delayed cellar neural networks (FOTDCNNs) that characterize real environments, this article introduces partial uncertainties, fuzzy operators, and nonlinear activation functions into the network models. Specifically, both the fuzzy AND operator and the fuzzy OR operator are contemplated in the master–slave systems. In response to the properties of the considered cellar neural networks (NNs), this article designs a new class of mixed control protocols that utilize both the error feedback information of systems and the sampling information of impulse moments to achieve network synchronization tasks. This approach overcomes the interference of time delays and uncertainties on network stability. By integrating the fractional-order comparison principle, fractional-order stability theory, and hybrid control schemes, readily verifiable asymptotic synchronization conditions for the studied fuzzy cellar NNs are established, and the range of system parameters is determined. Unlike previous results, the impulse gain spectrum considered in this study is no longer confined to a local interval (−2, 0) and can be extended to almost the entire real number domain. This spectrum extension relaxes the synchronization conditions, ensuring a broader applicability of the proposed control schemes.