Secure State Estimation for Continuous-Time Cyber-Physical Systems Under Stochastic Attacks and Faults

This article studies the secure state estimation problem of continuous-time cyber-physical systems affected by sensor attacks and actuator faults, where the attackers do not target fixed transmission channels but instead stochastically select the channels to attack at each moment based on a specific Markov process. To address these challenges, a reduced-order observer is designed to simultaneously estimate the original system states, faults, and attacks, while ensuring that its observation errors remain unaffected by these faults, attacks, and unknown disturbances. According to the stability theory of stochastic systems, a necessary and sufficient condition is provided for the stochastic stability of the observation error system under known transition rates, with further analysis of its stability under unknown transition rates. Finally, the validity and superiority of the proposed method are verified through two numerical examples.