Reachable set control for nonlinear Markov jump cyber–physical systems with false data injection attacks

This paper presents the problem of reachable set controller design for a class of nonlinear Markov jump cyber–physical systems (MJCPSs). The adverse effects of bounded peak external disturbances, uncertainties and false data injection (FDI) attacks with certain probability on MJCPSs are considered. The aim is to design an appropriate controller to guarantee that the actual state of the closed-loop MJCPSs is defined by a specified set. Firstly, the Lyapunov functional method is introduced because the time-varying delays are carried by FDI attacks. By using the Lyapunov functional method, an ellipsoid description of the reachable set containing all the states of the system originating from the origin is obtained. Then, the controller gain can be obtained via a set of feasible linear matrix inequalities (LMIs). Finally, the effectiveness of the designed reachable set controller is proved by simulation results.