In this paper we give a Lyapunov functional characterization of h-stability for nonlinear dynamic systems on time scales under the condition of u ∞ -similarity between their variational systems. Furthermore, we give some examples related to the notions of u ∞ -similarity and h-stability.

Abstract. In this paper, we investigate uniform Lipschitz and asymptotic stability for perturbed differential systems using integral inequalities.

We study boundedness of solutions of dynamic equations on time scales by using Lyapunov-type functions.

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In this paper we study the impulsive stabilization of dynamic equations on time scales via the Lyapunov’s direct method. Our results show that dynamic equations on time scales may beψ-exponentially stabilized by impulses. Furthermore, we give some examples to illustrate our results.