H∞$$ {H}_{\infty } $$ Control for Markov Jump Systems With Partially Unknown Transition Probabilities Under Denial‐Of‐Service Attacks

ABSTRACT This article investigates the control problem of discrete‐time Markov jump systems under aperiodic denial‐of‐service attacks. A hidden Markov model is introduced to construct an asynchronous controller to address the mode mismatch between the system and the controller. To handle the partially unknown transition probabilities, corresponding linear matrix inequality conditions are formulated to address the associated uncertainties. A piecewise Lyapunov function is constructed by analyzing the duration and frequency constraints of denial‐of‐service attacks. An iterative approach is further proposed to derive sufficient conditions to guarantee the performance of the system under aperiodic denial‐of‐service attacks. The controller gain matrix is computed by solving a set of linear matrix inequalities. Finally, the effectiveness of the proposed theoretical framework is demonstrated through numerical simulations.