Sliding mode control for nonlinear Markovian jump systems under denial-of-service attacks

This paper investigates the sliding mode control ( SMC ) problem for a class of discrete-time nonlinear networked Markovian jump systems ( MJSs ) in the presence of probabilistic denial-of-service ( DoS ) attacks. The communication network via which the data is propagated is unsafe and the malicious adversary can attack the system during state feedback. By considering random Denial-of-Service attacks, a new sliding mode variable is designed, which takes into account the distribution information of the probabilistic attacks. Then, by resorting to Lyapunov theory and stochastic analysis methods, sufficient conditions are established for the existence of the desired sliding mode controller, guaranteeing both reachability of the designed sliding surface and stability of the resulting sliding motion. Finally, a simulation example is given to demonstrate the effectiveness of the proposed sliding mode control algorithm.