Synchronization control of delayed Markov Jumping Neural Networks under Hybrid Network Attacks

This study addresses the synchronization control problem for Markov jump neural networks subject to hybrid cyber attacks by devising a control strategy that ensures master-slave system synchronization. The stochastic occurrences of deception attacks and denial-of-service (DoS) attacks are characterized using independent Bernoulli-distributed sequences, integrating the dynamics of the hybrid attack mechanisms within a unified framework. A Lyapunov-Krasovskii functional is constructed employing the free-weighting matrix approach. Utilizing linear matrix inequality (LMI) analysis techniques and specific integral inequality bounding methods, sufficient conditions are derived to guarantee the stochastic mean-square stability of the synchronization error system while satisfying prescribed performance indices. Furthermore, an effective matrix decoupling technique is employed to address the coupled terms within the system matrices, and the controller parameters are obtained using the LMI toolbox in MATLAB. Finally, numerical simulations are conducted to validate the feasibility and effectiveness of the proposed methodology. Simulation results demonstrate that the designed controller successfully drives the synchronization error signals under hybrid attacks to converge asymptotically to zero, thereby achieving synchronization between the master and slave neural network systems.