This article addresses the issue of \(H_{\infty }\) filtering for Markov jump Roesser systems based on a 2-D event-triggered mechanism, in which both the probability information of the system mode and the probability information of the observation mode are partially known. Aiming at the problem of the mismatch phenomenon between system mode and filter mode, an asynchronous filter based on a hidden Markov model is designed. Meanwhile, in order to reduce the amount of data transmission and make more rational use of communication resources, an observed-mode-based 2-D event-triggered mechanism is established. Subsequently, the \(H_{\infty }\) performance analysis criteria for 2-D Markov jump systems are constructed. Moreover, the design method of an asynchronous filter for 2-D Markov jump systems based on a hidden Markov model is established. In the design of the filter, two adjustable parameters are introduced to obtain less conservative conditions when solving the filter gain and reducing the conservatism of the designed filter. Finally, the validity and superiority of the designed filter can be certified by an illustrative example and an example of heat exchange between the heating flow in a tube.
