Event-Based Synchronization for Markov Jump Neural Networks

This paper investigates the problem of synchronization of discrete-time neural networks (NNs) with Markov switching topologies. Firstly, the stochastic variations in the mode transition probabilities (TPs) that exhibit time-varying characteristics within a finite set are taken into account. These variations are governed by a higher-level homogeneous Markov chain. Secondly, an adaptive event-triggered (ET) mechanism is introduced to improve the utilization efficiency of network resources. Unlike conventional deterministic ET mechanisms, the introduced ET mechanism is formulated based on stochastic dynamic variables, thereby offering a more flexible and responsive approach to data transmission. Subsequently, sufficient conditions for $H_{\infty}$ synchronization of Markov Jump NNs are established by exploiting the Lyapunov stability theory. Finally, the validity of the proposed control scheme is confirmed by a simulation example.