The problem of delay‐dependent stability is concerned for two‐dimensional discrete‐time systems with interval time‐varying delays in this paper. Choosing a Lyapunov functional with the upper bound and lower bound of delays, considering all terms in the difference and using two‐dimensional Abel lemma‐based finite‐sum inequalities, a new delay‐dependent stability criterion in terms of linear matrix inequality is derived for two‐dimensional discrete‐time systems. Then, based on the delay‐dependent stability criteria, a state feedback control problem and a dynamic output feedback control problem are considered to realize the stability control for the two‐dimensional discrete‐time system. Finally, it is shown through four numerical examples that the stability criterion can provide a larger admissible maximum upper bound with less decision variables than the stability criterion using two‐dimensional Jensen inequalities approach.

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