@article{Damak_Hammami_Kicha_2021, title={A converse theorem for practical $h$-stability of time-varying nonlinear systems}, volume={50}, url={https://nzjmath.org/index.php/NZJMATH/article/view/79}, DOI={10.53733/79}, abstractNote={<p>This paper treats the concept of practical uniform $h$-stability for such perturbed dynamical systems as an extension of practical uniform exponential stability. We present a converse Lyapunov theorem and we give sufficient conditions that guarantee practical uniform $h$-stability for a time-varying perturbed system using the Gronwall-Bellman inequality and Lyapunov’s theory. Some examples are introduced to illustrate the applicability of the main results.</p>}, journal={New Zealand Journal of Mathematics}, author={Damak, H. and Hammami, M. A. and Kicha, A.}, year={2021}, month={Feb.}, pages={109–123} }