The research presented here uses the sliding mode control (SMC) method to explore the observer-based asynchronous \({{H}_{\infty }}\) control problem for hidden Markov jump systems with incomplete transition probabilities and actuator malfunction. Firstly, a sliding surface (SS) function that depends on mode due to hidden the current non-synchronization phenomenon of jump modes between the system and the controller is taken into account when designing the Markov model. According to the observer design theory, the state tracks should be forced upon the selected SS within a predetermined, time-limited window using an asynchronous SMC rule with quantized measurements. Secondly, in order to guarantee necessary \({{H}_{\infty }}\) performance in both the phases of reaching and sliding action, suitable requirements for finite-time boundedness are stated. Finally, to attest to the availability and viability of the results given, two simulation outcomes are given.
