Composite Antidisturbance $\mathcal {H}_{\infty }$ Control for Hidden Markov Jump Systems With Multi-Sensor Against Replay Attacks

This article discusses the problem of composite
$\mathcal {H}_{\infty }$
control for hidden Markov jump systems subject to replay attacks. Since it is difficult to obtain the mode information of the system directly in practice, a hidden Markov model is adopted to facilitate subsequent works. The hidden state represents the actual system dynamics that cannot be known exactly, but can be observed by the detector. Considering the multi-disturbance phenomenon, one of which is norm bounded and another is produced by an exogenous system, a composite
$\mathcal {H}_{\infty }$
control scheme based on disturbance observer is designed to improve the antidisturbance ability of the system. In addition, with the help of multi-sensor approach, a detection scheme, revealing the attacker's tactics and determining which sensor is assaulted, is presented to withstand replay attacks. Then, a composite disturbance observer-based controller, ensuring that the resulting system is stochastically stable with an expected
$\mathcal {H}_{\infty }$
performance under replay attacks, is designed by solving convex optimization problems. Finally, the effectiveness and superiority of the developed method are verified by an example.