A new weighted quasi-balanced model reduction method for two-dimensional discrete systems with input and output weights is developed. The development of the new method can be divided into three distinct stages. First is the introduction of four auxiliary Lyapunov equations by which weighted controllability and observability quasi-gramians are defined. The second is the computation of the weighted quasi-gramians. The third is the definition of the weighted quasi-balanced realization. A 2-D filter of order
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