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The paper presents a stability criterion and a method for computing the H∞ norm of 2D discrete systems. Both methods are based on linear matrix inequalities (LMI), and, hence, they are computationally tractable. In deriving these methods, the finite-order Fourier series approximation of the solution for frequency-dependent LMI (FDLMI), and the properties of the quadratic form representation of finite-order Fourier series play key roles. From the point of view of the proposed methods, existing LMI-based methods can be regarded as ones which are obtained by the Fourier series approximation of order zero, and thus, it is expected that the proposed methods lead to less conservative results. This is illustrated by numerical examples. The effectiveness of the proposed methods is also illustrated by numerical examples.