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

Key Points

• This research investigates the conditions for Hyers-Ulam stability and relative controllability in linear matrix discrete systems with a single delay.
• Derived conditions for Hyers–Ulam and Hyers–Ulam–Rassias stability using norm estimation of an auxiliary matrix function.
• Established a necessary condition for relative controllability with the delayed Gram matrix.
• Provided an illustrative example to validate the theoretical results.
• Sufficient conditions for Hyers–Ulam stability were successfully derived.
• A necessary condition for relative controllability was established using Gram matrix properties.