Stability and Stabilization of Semi-Markov Jump Linear System With DoS Attacks

In this brief, the denial of service (DoS) attacks on the communication channel of the semi-Markov jump system are studied. Firstly, the DoS attacks are modeled as a Markov chain, and then a networked semi-Markov jump system model with DoS attacks is proposed. Based on this model, the network semi-Markov jump system stability under the DoS attacks is analyzed, and the mean square stability lemma is derived. According to the mean square stability condition of the system, the sufficient condition of the mean square stability of the system is put forward, and the mean square stability controller is designed according to the sufficient condition. Due to the introduction of the DoS attacks, a new Lyapunov function is constructed, and linear matrix inequality(LMI) is derived. Finally, several groups of comparative simulation are constructed to verify the compensation effect of control strategy on DoS attacks and frequent system switching.