Finite-time dynamic-memory event-triggered ℋ _∞ control of stochastic multi-agent systems with randomly occurring nonlinearities and actuator faults under semi-Markov switching topologies

This paper investigates the finite-time dynamic memory event-triggered ℋ ∞ leader–follower bounded consensus problem for multi-agent systems under semi-Markov switching topologies, actuator faults, and stochastic nonlinearities. First, to enhance the practicality of the system model, we comprehensively incorporate practical factors including randomly occurring nonlinearities and actuator faults while proposing a novel definition of stochastic finite-time bounded consensus. By designing an asynchronous controller, we prove that the system can achieve finite-time ℋ ∞ leader–follower bounded consensus. Second, we further consider the scenario where system matrices contain uncertainties. Under the proposed asynchronous controller and the new definition, the finite-time ℋ ∞ leader–follower bounded consensus is analytically guaranteed. The main contribution lies in employing a dynamic memory event-triggered mechanism to address the potential missing identification of actuator faults due to sampling-induced limitations. Finally, numerical simulations are used to verify the effectiveness and reliability of the theoretical results.