H-Stability of Dynamic Systems on Time Scales

H-stability is an important development of the notion of exponential asymptotic stability. The notion of h-stability was introduced with the intention of obtaining the stability for a weaker stable system under some perturbations. In this paper, first, we introduce the background, the current situation of studies for h-stability. Second, we give some definition about time scales and h-stability. Finally, we give some sufficitent conditions for the h-stability of a trivial solution of nonlinear pertured dynamic systems on time scales via Lyapunov method and comparison principle.