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This paper addresses the state observer problem for discrete two-dimensional (2-D) systems with delays described by the Roesser model. The main objective of the design is to ensure asymptotic stability by designing a 2-D observer. It sounds like the paper is proposing a new method for designing a 2-D observer for a given system. The method is based on two key concepts: the Lyapunov function and the linear matrix inequalities (LMIs) formalism. The example is utilized to showcase how the method can be practically applied to a given system and to evaluate the observer’s performance.