Mean square exponential stabilisation for directional 2D Roesser hidden Markov model

Based on the two-dimensional (2D) Roesser model, this paper focuses on the asynchronous controller design for directional 2D Markov jump systems (MJSs). Considering the more practical situation that the modes of the 2D MJSs in the horizontal and vertical directions are independent, and the system modes are asynchronous with that of the controller, the directional 2D MJSs are proposed and the asynchronous controller is designed, respectively. Based on the Lyapunov theory, a sufficient condition for the mean square exponential stability of the controlled directional 2D MJSs is given. Moreover, the partially unknown transition probabilities in systems and controllers are considered. Finally, an example is given to illustrate that the proposed method is effective.

Automated summary

This paper focuses on the asynchronous controller design for directional 2D Markov jump systems (MJSs) based on the two-dimensional Roesser model. The proposed method considers the independent modes of the 2D MJSs in the horizontal and vertical directions and addresses the asynchronous relationship between the system modes and the controller modes. The paper provides a sufficient condition for the mean square exponential stability of the controlled directional 2D MJSs based on Lyapunov theory, while also considering partially unknown transition probabilities in systems and controllers. An example is given to demonstrate the effectiveness of the proposed method.