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New Stability Conditions for a Class of Nonlinear Discrete-Time Systems with Time-Varying Delay

Author

Listed:
  • Sami Elmadssia

    (Higher Institute of Applied Sciences and Technology University of Gafsa, Gafsa 2112, Tunisia
    SYS’COM Laboratory, National Engineering School of Tunis (ENIT), Belvedere 1002, Tunisia)

  • Karim Saadaoui

    (Department of Computer Engineering, College of Computers and Information Technology, Taif University, Taif 888, Saudi Arabia
    LARA Laboratory, National Engineering School of Tunis (ENIT), University of Tunis ElManar, Belvedere 1002, Tunisia)

Abstract

In this paper, the stability problem of discrete time delay systems is investigated. The class of systems under consideration is represented by delayed difference equations and models nonlinear discrete time systems with time varying delay. It is transformed into an arrow from matrix representation which allows the use of aggregation techniques and M-matrix properties to determine novel sufficient stability conditions. The originalities of our findings are shown in their explicit representation, using system’s parameters, as well as in their easiness to be employed. The obtained results demonstrate also that checking stability of nonlinear discrete time systems with time varying delay can be reduced to an M-matrix test. Next, it is shown how to use our method in designing a state feedback controller that stabilizes a discrete time Lure system with time varying delay and sector bounded nonlinearity. Finally, several examples are provided to show the effectiveness of the introduced technique.

Suggested Citation

  • Sami Elmadssia & Karim Saadaoui, 2020. "New Stability Conditions for a Class of Nonlinear Discrete-Time Systems with Time-Varying Delay," Mathematics, MDPI, vol. 8(9), pages 1-19, September.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1531-:d:410441
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    References listed on IDEAS

    as
    1. J. Diblík & M. Růžičková & Z. Å marda & Z. Å utá, 2012. "Asymptotic Convergence of the Solutions of a Dynamic Equation on Discrete Time Scales," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-20, January.
    2. S. Elmadssia & K. Saadaoui & M. Benrejeb, 2016. "New stability conditions for nonlinear time varying delay systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(9), pages 2009-2021, July.
    3. He, Zhimin & Lai, Xin & Hou, Aiyu, 2009. "Stability and Neimark–Sacker bifurcation of numerical discretization of delay differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2010-2017.
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    Cited by:

    1. Chun-Tang Chao & Ding-Horng Chen & Juing-Shian Chiou, 2021. "Stability Analysis and Robust Stabilization of Uncertain Fuzzy Time-Delay Systems," Mathematics, MDPI, vol. 9(19), pages 1-13, October.
    2. Thaned Rojsiraphisal & Piyapong Niamsup & Suriyon Yimnet, 2020. "Global Uniform Asymptotic Stability Criteria for Linear Uncertain Switched Positive Time-Varying Delay Systems with All Unstable Subsystems," Mathematics, MDPI, vol. 8(12), pages 1-18, November.

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