Resilient ${\mathcal{H}}_{\infty}$ Output Feedback Control for Hidden Semi-Markov Jump Systems Subject to Hybrid Cyber Attacks

In this paper, a novel hidden semi-Markov model (HS-MM) in the continuous-time domain is proposed, and theH∞static output feedback control problem for hidden semi-Markov jump linear systems (HS-MJLSs) is investigated. Data transmission via a wireless network medium in HS-MJLSs is vulnerable to cyber attacks. Therefore, we adopt a resilient control strategy to ensure the stability of HS-MJLSs under hybrid cyber attacks, factoring in both denial-of-service attacks and false data injection attacks. In comparison with the conventional Markov jump linear systems, the HS-MM proposed by us is more universal, which is reflected in the following two aspects: (i) The system mode is considered to be undetectable. The jumping of the controller depends on the observation mode, and is asynchronous with the jumping of the system mode. (ii) Both the mode jumps of the original system and controller are considered to be related to the sojourn-time, which is more reasonable than the memoryless jumping processes. By using the established HS-MM and a Lyapunov-based approach, some sufficient conditions are obtained to ensure the stochastic stability of the HS-MJLSs with anH∞performance and hybrid cyber attacks. Finally, the proposed theoretical results are demonstrated by two simulation examples.