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Sliding Mode Observer Based-Controller Design for Nonlinear Systems with Time Varying Delay

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Recent Results on Nonlinear Delay Control Systems

Part of the book series: Advances in Delays and Dynamics ((ADVSDD,volume 4))

Abstract

A class of nonlinear time varying delay systems in the presence of time delay uncertainties is considered in this chapter. The entries of the system input distribution matrix may be nonlinear functions of the outputs and time. Under mild limitations on the uncertainty, an observer is synthesised using sliding mode techniques such that the error dynamics are ultimately uniformly bounded in the presence of uncertainties and time delay. Then, a nonlinear control scheme is developed based on the estimated states, and a set of sufficient conditions is presented such that the corresponding closed-loop systems are uniformly ultimately bounded, using the well-known Lyapunov-Razumikhin approach. It is not required that the structure of the uncertainty be known. Finally, a numerical example is presented to demonstrate the approach and simulation results show the effectiveness of the developed paradigm.

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Author information

Authors and Affiliations

  1. Instrumentation, Control and Embedded Systems Research Group, School of Engineering and Digital Arts, University of Kent, Canterbury, Kent, CT2 7NT, UK

    Xing-Gang Yan

  2. CICESE Research Center, P.O. Box 434944, San Diego, CA, 92143-4944, USA

    Sarah K. Spurgeon & Yury Orlov

Authors
  1. Xing-Gang Yan
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  2. Sarah K. Spurgeon
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  3. Yury Orlov
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Corresponding author

Correspondence to Xing-Gang Yan .

Editor information

Editors and Affiliations

  1. Department of Mathematics, National Technical University of Athens, Athens, Greece

    Iasson Karafyllis

  2. Department of Mathematics, Louisiana State University (LSU), Baton Rouge, Louisiana, USA

    Michael Malisoff

  3. CNRS-CentraleSupélec-Université Paris Sud, EPI Inria “DISCO”, Laboratory of Signals and Systems (L2S, UMR CNRS 8506), Gif-sur-Yvette, France

    Frederic Mazenc

  4. Department of Information Engineering, Computer Science, and Mathematics, University of L’Aquila, L’Aquila, Italy

    Pierdomenico Pepe

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Yan, XG., Spurgeon, S.K., Orlov, Y. (2016). Sliding Mode Observer Based-Controller Design for Nonlinear Systems with Time Varying Delay. In: Karafyllis, I., Malisoff, M., Mazenc, F., Pepe, P. (eds) Recent Results on Nonlinear Delay Control Systems. Advances in Delays and Dynamics, vol 4. Springer, Cham. https://doi.org/10.1007/978-3-319-18072-4_18

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  • DOI: https://doi.org/10.1007/978-3-319-18072-4_18

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-18071-7

  • Online ISBN: 978-3-319-18072-4

  • eBook Packages: EngineeringEngineering (R0)

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