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Stability analysis of two-dimensional (2-D) discrete systems is a problem of considerable importance in both theory and practical applications. The 2-D linear state-space models were first introduced in 1970's by several researchers. Among these models, the most general model for 2-D discrete systems was proposed by Fornasini and Marchesini in 1976, commonly known as Fornasini-Marchesini (FM) first model. A survey of the existing literature on the stability of 2-D discrete systems described by the FM first model is presented.