Abstract
This work explores generalized Ulam‐type stability for a family of time‐lag discrete systems governed by two‐order difference operators. First and foremost, we put forward strict mathematical formulations of Hyers–Ulam‐based generalized stability adapted to the above‐mentioned two‐order time‐delay discrete frameworks, which expand existing stability theories for lower‐order discrete dynamic models. Afterwards, utilizing the discrete matrix delay exponential approach alongside the discrete Grönwall inequality, we rigorously deduce adequate criteria that ensure such generalized stability characteristics for the investigated systems, with core theoretical deductions elaborated thoroughly. In the end, a numerical case is designed to demonstrate the correctness and applicability of our derived theoretical outcomes and further verify the reliability of the established analytical strategies.