Hyers–Ulam stability and relative controllability of a linear matrix discrete system with single delay

This paper focuses on the Hyers-Ulam stability and relative controllability of a linear matrix discrete system with single delay. By utilizing the norm estimation of an auxiliary matrix function, sufficient conditions for both Hyers–Ulam stability and Hyers–Ulam–Rassias stability are derived. Additionally, a necessary condition for relative controllability is established using the delayed Gram matrix. Finally, a detailed illustrative example is provided to validate the theoretical results.