A converse theorem for practical $h$-stability of time-varying nonlinear systems

Authors

  • H. Damak University of Sfax
  • M. A. Hammami University of Sfax
  • A. Kicha University of Sfax

Keywords:

Lyapunov function, Practical uniform $h$-stability, semi-global practical uniform $h$-stability, Time-varying systems

Abstract

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.

Downloads

Download data is not yet available.

Author Biographies

H. Damak, University of Sfax

University of Sfax,
Faculty of Sciences of Sfax,
Tunisia

M. A. Hammami, University of Sfax

University of Sfax,
Faculty of Sciences of Sfax,
Tunisia

A. Kicha, University of Sfax

University of Sfax,
Faculty of Sciences of Sfax,
Tunisia

Downloads

Published

2021-02-04

How to Cite

Damak, H., Hammami, M. A., & Kicha, A. (2021). A converse theorem for practical $h$-stability of time-varying nonlinear systems. New Zealand Journal of Mathematics, 50, 109-123. Retrieved from https://www.nzjmath.org/index.php/NZJMATH/article/view/79

Issue

Section

Articles