Observer Design for Cyber-Physical Systems With State Delay and Sparse Sensor Attacks

This paper studies the problem of the secure state estimation of cyber-physical systems. The system model we studied is a class of discrete-time systems with state delay and sparse sensor attacks. In the design of the observer, a Projection Operator is utilized to determine the correct attack set, and the gain matrix will be switched accordingly. In this way, the excessive estimation error could be avoided effectively. In addition, based on the generalization of the classical Krasovskii Stability Theorem for stability analysis of time-delay systems, a Lyapunov-Krasovskii functional is chosen and a sufficient condition for the existence of the observer together with its design method is determined. The designed observer overcomes the difficulties caused by state delay and sensor attacks, and has good performance in secure estimation. Finally, two examples are given to verify that the observer can restore the desired estimate in a short time when a sudden attack occurs.