Dynamic Event-Triggered Synchronization Control for Hidden Markov Jump Neural Networks Subject to Time-Varying Delay

This paper investigates the synchronization control problem of continuous hidden Markov jump neural networks (MJNNs) with time-varying delay (Td). Due to the challenge of accurately obtaining the system’s mode information in real-world environments, the mode transitions of the original system are detected using a hidden Markov model. Subsequently, a controller is designed based on the detected mode information. To optimize the utilization of network resources and reduce the redundant data transmission, a dynamic event-triggered mechanism (DETM) is adopted. Then, through the application of Lyapunov stability theory, the delay-dependent Lyapunov functional is constructed and some sufficient conditions which ensure the system achieves stochastic stability and meet the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> performance index <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\eta $ </tex-math></inline-formula> are established. Lastly, the feasibility of the method is validated through an example.