The asynchronous \(H_{\infty }\) sampled data control problem is examined in this manuscript for continuous-time interval type-2 (IT2) fuzzy nonlinear Markov jump systems (MJSs) susceptible to cyberattacks. The system and controller modes are asynchronous. A hidden Markov model (HMM) is employed to observe the modes of the original system. The goal is to design an asynchronous controller based on HMM and quantum genetic algorithm (QGA) to ensure the closed-loop IT2 MJSs is stochastically stable with \(H_{\infty }\) attenuation level \(\vartheta \) in the context of random controller gain fluctuation and the system modes hiding for the controller. Linear matrix inequality (LMI) has been utilized to get adequate stability criteria using looped stochastic Lyapunov–Krasovskii functionals (SLKFs). Additionally, QGA is used to optimize the control gain matrices. A Bernoulli distribution regulates the deception attack in the actuator. At last, the findings are verified using mass spring damper system for practical applicability.
