On the Stability of Linear Quaternion-Valued Differential Equations

This paper deals with the stability of linear quaternion-valued differential equations. First, we derive an explicit norm estimation like the matrix exponential function in the sense of quaternion-valued. Second, we use this norm to show that the first-order linear equations are asymptotically stable and Hyers–Ulam’s type stable. Further, we show that nth-order equations are also generalized Hyers–Ulam stability. Some examples which can effectively illustrate the theoretical results are presented.