Observer-Based Neural Sliding Mode Control of Fuzzy Markov Jump Systems via Dynamic Event-Triggered Approach

This study addresses the challenge of designing an event-triggered observer for neural network-enhanced sliding mode control in nonlinear Takagi–Sugeno fuzzy Markov jump systems, where premise variables are not directly measurable. Firstly, for the purpose of state observer design, a dynamic event-triggered mechanism integrated with a neural network-based compensator is developed. Secondly, through the construction of an integral sliding surface, the dynamic behaviors of both the sliding mode and the error system are formulated, incorporating estimated premise parameters. Thirdly, rigorous stochastic stabilization criteria are established, incorporating H∞ disturbance attenuation with a specified level γ, while accounting for transition rates with general uncertainty characteristics. Subsequently, a fuzzy adaptive sliding mode control scheme is synthesized to ensure finite-time convergence of the system states to the predefined sliding surface. Finally, the effectiveness of the proposed control strategy is thoroughly validated through high-fidelity numerical simulations on a practical example.