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Absolute stability of nonlinear systems with two additive time-varying delay components

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Abstract

In this paper, we present a new sufficient condition for absolute stability of Lure system with two additive time-varying delay components. This criterion is expressed as a set of linear matrix inequalities (LMIs), which can be readily tested by using standard numerical software. We use this new criterion to stabilize a class of nonlinear time-delay systems. Some numerical examples are given to illustrate the applicability of the results using standard numerical software.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Higher Institute of Applied Sciences and Technology of Gabès, Street Amor Ben El Khatab, 6029, Gabès, Tunisia

    Bassem Ben Hamed

  2. Department of Electrical Engineering, National Engineering School of Sfax, Street Soukra km 3.5, B.P. 1173, 3038, Sfax, Tunisia

    Mohamed Chaabane & Walid Kacem

Authors
  1. Bassem Ben Hamed
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  2. Mohamed Chaabane
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  3. Walid Kacem
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Corresponding author

Correspondence to Bassem Ben Hamed.

Additional information

Bassem Ben Hamed received the master degree in mathematics from Paul Sabatier University, Toulouse, France in 2003. He received the doctorate degree in mathematics from Paul Sabatier University, Toulouse, France, and from University of Sfax, Sfax, Tunisia in 2006. He is now an associate professor in Higher Institute of Applied Sciences and Technology of University of Gabès, Tunisia.

His research interests include time-delay systems, robust control, neutral networks, singular systems, Painlevée equations, isomonodromic deformations, and integrability of Hamiltonian systems.

Mohamed Chaabane received the doctorate degree in electrical engineering from University of Nancy, France in 1991. In 2005, he obtained the University Habilitation degree from National School of Engineers of Sfax, Tunisia. He is the editor in chief of the International Journal on Sciences and Techniques of Automatic Control and Computer Engineering. He is currently a professor in automatic control at Preparatory Institute of Engineers of Sfax, Tunisia. He is a member of Automatic Control Unit (research group) of National School of Engineers of Sfax, Tunisia.

His research interests include robust control, optimal control, linear matrix inequalities, descriptor systems, and applications of theses techniques to fed-batch processes and agriculture systems.

Walid Kacem received the master degree and the doctorate degree in automatic control from National School of Engineers of Sfax, Tunisia in 2003 and 2009, respectively. He is now an associate professor at the Faculty of Sciences of Sfax.

His research interests include delay systems, stability and stabilization of continuous systems, and their applications.

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Hamed, B.B., Chaabane, M. & Kacem, W. Absolute stability of nonlinear systems with two additive time-varying delay components. Int. J. Autom. Comput. 8, 391–402 (2011). https://doi.org/10.1007/s11633-011-0596-y

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  • DOI: https://doi.org/10.1007/s11633-011-0596-y

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