$H_{\infty}$ Observer-Based Control for Markov Jump System Under Protocol-Based DoS Attacks

This paper addresses the $H_{\infty}$ observer-based control problem for discrete-time Markov jump systems subjected to DoS attacks. To enhance the effectiveness of the attack, a protocol-based DoS attacks mechanism is constructed, which relies on the current transmitted signals and the latest un-attacked signals. With the attacks strategy, the adversary possesses the capability to dynamically adjust the quantity of attacked nodes according to the importance degree of measurement outputs. Moreover, a hidden Markov model is employed to characterize the asynchronous behavior between the observer-based controller and the plant. Then, sufficient conditions are derived to guarantee the stochastic stability of the system and provide the design approach for the asynchronous controller. Finally, a boost converter circuit is utilized to demonstrate the effectiveness of the proposed scheme.