Orbital Hausdorff dependence and stability of the solution to differential equations with variable structure and non-instantaneous impulses

Abstract In this paper, we investigate the orbital Hausdorff continuous dependence and stability of the solution to differential equations with variable structure and non-instantaneous impulses. The concepts of orbital Hausdorff continuous dependence and stability are used to characterize the relations of solution corresponding to the impulsive moments and the difference between the impulsive moments and the junction points in the sense of the Hausdorff distance. Then, we establish sufficient conditions to guarantee the orbital Hausdorff continuous dependence and stability on their respective trajectories. Finally, two examples are given to illustrate our theoretical results.