The generalized invariance principle for dynamic equations on time scales

The study of long-term behavior of a solution generated by dynamics on time scales always gains a great amount of attentions both from Engineers and from mathematicians. In the paper, a generalized invariance principle, which not only includes the case described by the conventional invariance principle but also involves the case where the sign of the Delta derivative of the Lyapunov function along with the solution is not determined, is established. This consequently allows us to verify the stability and boundedness of the solution generated by a much wider class of dynamic equations on time scales by utilizing this generalized principle.