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State-Dependent Switching Law for Stabilization to a Switched Time-Delay System with Two Unstable Subsystems

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Advances in Nonlinear Dynamics

Part of the book series: NODYCON Conference Proceedings Series ((NCPS))

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Abstract

In this chapter, a design method of state-dependent switching law is proposed to stabilize a class of switched delay systems with two unstable subsystems. With a free-chosen short delay, the delayed subsystems are first approximated to the form of second-order mechanical systems by using an invertible transformation and second-order Taylor expansion. Then, a performance index associated with the energy functions of the approximate subsystems is defined, and two switching curves are determined from the Euler equation derived by applying the variational principle. With a switching law designed in this way, the original switched delay systems can be stabilized to the unique equilibrium or to periodic solutions, although the two original subsystems are unstable for any delay values, as shown in the illustrative examples.

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Acknowledgements

The first author was supported by NSF of China under Grant 11802065, the Science and Technology Program of Guizhou Province ([2018]1047), the fund project of Key Laboratory of Advanced Manufacturing Technology, Ministry of Education, Guizhou University (KY[2018]478). The second author was supported by NSF of China under Grant 12072370.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Guizhou University, Guiyang, China

    Yusheng Zhou

  2. State Key Lab of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, China

    Zaihua Wang

Authors
  1. Yusheng Zhou
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  2. Zaihua Wang
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Corresponding author

Correspondence to Zaihua Wang .

Editor information

Editors and Affiliations

  1. Department of Structural and Geotechnical Engineering, Sapienza University of Rome, Rome, Italy

    Walter Lacarbonara

  2. Department of Mechanical Engineering, University of Maryland, College Park, MD, USA

    Balakumar Balachandran

  3. Department of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, USA

    Michael J. Leamy

  4. Department of Physics, Lanzhou University of Technology, Lanzhou, Gansu, China

    Jun Ma

  5. ISEP-Institute of Engineering, Polytechnic of Porto, Porto, Portugal

    J. A. Tenreiro Machado

  6. Department of Applied Mechanics, Budapest University of Technology and Economics, Budapest, Hungary

    Gabor Stepan

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Zhou, Y., Wang, Z. (2022). State-Dependent Switching Law for Stabilization to a Switched Time-Delay System with Two Unstable Subsystems. In: Lacarbonara, W., Balachandran, B., Leamy, M.J., Ma, J., Tenreiro Machado, J.A., Stepan, G. (eds) Advances in Nonlinear Dynamics. NODYCON Conference Proceedings Series. Springer, Cham. https://doi.org/10.1007/978-3-030-81162-4_77

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  • DOI: https://doi.org/10.1007/978-3-030-81162-4_77

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-81161-7

  • Online ISBN: 978-3-030-81162-4

  • eBook Packages: EngineeringEngineering (R0)

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