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Practical stabilization of a class of uncertain time-varying nonlinear delay systems

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Abstract

In this paper we deal with a class of uncertain time-varying nonlinear systems with a state delay. Under some assumptions, we construct some stabilizing continuous feedback, i.e. linear and nonlinear in the state, which can guarantee global uniform exponential stability and global uniform practical convergence of the considered system. The quadratic Lyapunov function for the nominal stable system is used as a Lyapunov candidate function for the global system. The results developed in this note are applicable to a class of dynamical systems with uncertain time-delay. Our result is illustrated by a numerical example.

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Authors and Affiliations

  1. Département de Mathématiques, Institut Supérieur des Sciences Appliquées et de Technologie de Gabès, Rue Amor Ben El Khatab, 6029, Gabès, Tunisia

    Bassem Ben Hamed

  2. Département de Mathématiques, Faculté des Sciences de Sfax, BP 802, Route Soukra km 4, Sfax, 3018, Tunisia

    Mohamed Ali Hammami

Authors
  1. Bassem Ben Hamed
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  2. Mohamed Ali Hammami
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Bassem Ben HAMED was born in 1977. He received the M.S. degree in Mathematics from Paul Sabatier University, Toulouse, France in 2003. He received the Ph.D. degree in Mathematics from Paul Sabatier University, Toulouse, France and from the University of Sfax, Sfax, Tunisia in 2006. He is now an advisor assistant in Higher Institute of Applied Sciences and Technology of the University of Gabès, Tunisia. His current research interests are time-delay systems, robust control, neutral networks, singular systems, Painlevé equations, and isomonodromic deformations.

Mohamed Ali HAMMAMI received the “Doctorat” in Mathematics in 1994 from the University of Metz (France), the “Habilitation” in 2001 from the University of Sfax (Tunisia). He is currently a professor at the Faculty of Sciences of Sfax in the Department of Mathematics. His research interests are nonlinear control systems and differential equations (stability of time varying systems, stabilization of impulsive and time-delay systems, observability and observer).

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Hamed, B.B., Hammami, M.A. Practical stabilization of a class of uncertain time-varying nonlinear delay systems. J. Control Theory Appl. 7, 175–180 (2009). https://doi.org/10.1007/s11768-009-8017-2

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  • DOI: https://doi.org/10.1007/s11768-009-8017-2

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