Nonfragile H ∞ asynchronous control for 2-D Roesser systems with Markov model-based energy-limited DoS attacks

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This work addresses the nonfragile H ∞ issue of Roesser systems under the DoS attacks, in which the attacker's energy is limited. To describe the jumping behaviour of the normal operation mode and DoS attack mode, the Markov process is introduced. Compared with using the Bernoulli process to model DoS attacks, the Markov process is more general. A more realistic scenario, that is, by using the hidden Markov model to deal with the case, in which the mode information may not be accessible when the design control law. Meanwhile, the gain fluctuation of the controller is also considered. Then, by using the Lyapunov function, sufficient conditions are acquired to guarantee the stability for the 2-D systems with expected H ∞ performance index under the DoS attacks. Finally, the metal rolling process example is offered to verify the validity of the obtained theoretical results.