STABILITY OF QUATERNION-VALUED IMPULSIVE DIFFERENTIAL EQUATIONS

Abstract

We consider a class of quaternion-valued impulsive differential equations (QIDEs). We first use impulsive Cauchy matrices which are essential to explore the stability of QIDEs and whose exponential structure are analyzed in light of eigenvalues of matrices via the distance between impulsive points. Then, a number of sufficient criteria are acquired for the asymptotic stability of linear QIDEs and linear QIDEs with perturbation. In addition, the existence, uniqueness and Ulam–Hyers–Rassias stability of solutions of nonlinear QIDEs are investigated. Most importantly, the results which we obtain are presented in the sense of quaternion-valued and complex-valued, respectively. Finally, examples are given to indicate the utility of our theoretical results.