Secure State Estimation for Discrete CPSs with State Delay and Adversarial Attacks

In this paper, an observer is designed for cyber-physical systems (CPSs) modeled by a class of discrete-time systems with state delay and sparse actuator and sensor attacks. In the design, the original system is rewritten into a new form, which provides the basis for estimating the actuator and sensor attacks. And then a Projection Operator combined with the notion of orthogonal complement matrix is utilized to determine the correct attack sets. In addition, based on the Krasovskii Stability Theorem, a Lyapunov-Krasovskii functional is chosen and a sufficient condition for the existence of the observer together with its design method is determined. Finally, a numerical example is given to verify the effectiveness of the designed observer.