h-stability and boundedness results for solutions to certain nonlinear perturbed systems

In this work, we establish some new sufficient conditions to show the uni-formh-stability for nonlinear time-varying perturbed systems which can be viewedas an extension of the uniform exponential stability and polynomial stability. Also,we study the boundedness of solutions when the origin is not necessarily an equilib-rium point of the perturbed system. The idea is to use some Gronwall type integralinequalities. As an illustration, we present some examples with simulations to showthe applicability of the obtained results