Stabilization of Markov Jump Systems Under Replay Attacks

This paper investigates the stabilization problem of Markov jump systems under replay attacks. To accommodate the influence of attacks on information, a switching system is devised, focusing on attack signals. An extended space method is applied to organize the overall states and modes, including the delayed states and modes caused by attacks. By switching analysis methods, sufficient conditions are provided to ensure system stability. To solve the controller gains, a genetic algorithm is applied to handle the nonlinear terms in the given conditions. The designed method avoids the non-Markov jump caused by attacks and reduces the conservatism in solving processes. Finally, an example is given to verify the effectiveness of the designed approach.