Asynchronous Control of Markov Jump Systems Under Aperiodic DoS Attacks

The secure asynchronous control problem of Markov jump systems (MJSs) against aperiodic discrete denial-of-service (DoS) attacks is discussed in this brief. DoS attacks cut off the communication networks, resulting in the loss of state information. The impact of DoS attacks may cause mismatched behavior between controlled plant modes and controller modes, which can be illustrated by a hidden Markov model (HMM). An asynchronous controller is utilized to overcome the mismatched phenomenon. By employing multiple Lyapunov functions and iterative methods, and analyzing the conditions on malicious DoS attacks, sufficient conditions are derived to guarantee mean square stable of MJSs under aperiodic DoS attacks. By solving a set of linear matrix inequalities (LMIs), the asynchronous controller is designed. At last, the effectiveness of the proposed theoretical method is certified by a numerical simulation.