Protocol-Based State Estimation for 2-D Markov Jumping Systems With Randomly Occurring FDIAs

This article investigates the state estimation problem for 2-D Markov jumping systems subjected to randomly occurring false data injection attack. To address this challenge, a novel probabilistic multi-interval ETP (PMIETP) is proposed, integrated with a time-varying saturation mechanism (TVSM). The PMIETP is designed by combining subinterval triggering thresholds with a probability distribution model, thereby enhancing system performance and adaptability under varying network conditions. To further mitigate the impact of maliciously injected data and improve estimation robustness, a TVSM-based estimator is developed, which employs an adaptive threshold to confine abnormal data within an acceptable range. In addition, a particle swarm optimization algorithm is employed to fine-tune design parameters, thereby reducing the conservativeness of linear matrix inequality conditions. Based on Lyapunov stability theory, sufficient criteria are derived to guarantee mean-square asymptotic stability and prescribed noise attenuation performance. Finally, a numerical simulation example demonstrates the effectiveness and superiorities of the proposed approach over existing methods.