Practical semiglobal uniform exponential stability of nonlinear nonautonomous systems

  • A. Kicha University of Jijel, Faculty of Exact Sciences and Computer Sciences, Department of Mathematics, LAOTI Laboratory, Algeria
  • M. A. Hammami University of Sfax, Faculty of Sciences of Sfax, Department of Mathematics, Stability and Control of Systems and PDEs Laboratory, Tunisia
  • I.-E. Abbes University of Sfax, Faculty of Sciences of Sfax, Department of Mathematics, Stability and Control of Systems and PDEs Laboratory, Tunisia
Keywords: Lyaponov theory, Parametrized systems, Practical semi-global uniform exponential stability

Abstract

UDC 517.9

We solve the following twofold problem: In the first part, we deduce Lyapunov sufficient conditions for practical uniform exponential stability of nonlinear perturbed systems under  different conditions for the perturbed term. The second part presents a converse Lyapunov theorem for the notion of semiglobal uniform exponential stability for parametrized nonlinear time-varying systems. We establish the possibility of application of a perturbed parametrized system, by using Lyapunov theory, to the investigation of the robustness properties that may provide practical semiglobal uniform  exponential stability with respect to perturbations.

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Published
24.05.2023
How to Cite
KichaA., HammamiM. A., and AbbesI.-E. “Practical Semiglobal Uniform Exponential Stability of Nonlinear Nonautonomous Systems”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 75, no. 5, May 2023, pp. 596 -13, doi:10.37863/umzh.v75i5.7071.
Section
Research articles