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

Abstract

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