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In this article, an extended state observer‐based finite‐region control scheme is presented for two‐dimensional Markov jump systems with unknown mismatched disturbances. The mathematical model of the two‐dimensional Markov jump systems is built on the well‐known Roesser model. By establishing special recursive formulas and utilizing the 2‐D Lyapunov function theory, sufficient conditions are obtained, which prove that the resultant system is finite‐region bounded, if some linear matrix inequalities are achieved. Then, we provide an algorithm to solve the extended state observer‐based controller gains. With the proposed control scheme, the external disturbances can be actively rejected from the system outputs. To conclude, a numerical example based on the Darboux equation is provided to demonstrate the validity and effectiveness of the devised control scheme. [ABSTRACT FROM AUTHOR]

This paper addresses finite-region asynchronous H ∞ filtering for a class of two-dimensional Markov jump systems (2-D MJSs). A mathematical model is established using the Roesser model, and asynchrony is accounted for using a hidden Markov model (HMM). The modes jumping between the target system and the designed filter are determined by the given conditional probability matrix. Sufficient conditions are derived using suitable Lyapunov function and linear matrix inequalities (LMIs) to ensure stable filtering performance. The practical applicability of the approach is illustrated by two examples. Overall, this study offers a method to tackle filtering challenges in 2-D Markov jump systems, incorporating HMM, Lyapunov functions, and LMIs to effectively solve the finite-region asynchronous H ∞ filtering problem. • An HMM is used to describe the asynchronous phenomenon between the system and the filter. • Lyapunov functional and recursive formulas effectively analyze the FRB of filtering error system. • The Darboux equation and the heat exchange process both validate the effectiveness of the filter. [ABSTRACT FROM AUTHOR]