Secure control for discrete-time hidden Markov jump systems subject to replay attacks via output feedback

This paper investigates the static output feedback secure control problem for discrete-time hidden Markov jump systems against replay attacks. The main purpose is to realise that closed-loop systems are stochastically stable with or without replay attacks. Firstly, the tampered sensors under replay attacks can be identified via the proposed detection method. Then, an asynchronous static output feedback controller is designed, which can eliminate the negative impact caused by replay attacks in view of the detection results. Based on the linear matrix inequality technique, some sufficient conditions which ensure the closed-loop systems are stochastically stable and meet a given H∞ performance are established. Finally, a numerical example and a practical example are given to verify the effectiveness and superiority of the proposed method.