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State Feedback, Performance, and Robustness

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Analysis and Synthesis of Nonlinear Control Systems

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 408))

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Abstract

This chapter investigates state feedback design for models with a convex structure such as TS, polynomial, and descriptor; LFT is left for the next chapter. Similar to stability analysis, Lyapunov’s direct method and convexity are combined to derive sufficient stabilisation conditions. Based on the assumption that both the plant states and the membership functions are available, a variety of controller structures is presented along with quadratic and non-quadratic Lyapunov functions.

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Notes

  1. 1.

    Throughout the chapter, all the numerical values are rounded to two decimal places.

  2. 2.

    For numerical integration, the ode45 MATLAB\(^{\text{\textregistered }}\)function has been used.

  3. 3.

    For the ease of notation, the explicit time dependence is omitted.

  4. 4.

    A full video of the session is available at https://pod.uphf.fr/video/1583-discrete-reference-tracking-control-to-swing-up-an-electric-wheelchair/

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Authors and Affiliations

  1. Department of Electrical and Electronics Engineering, Sonora Institute of Technology, Obregon, Sonora, Mexico

    Miguel Bernal

  2. Instituto Universitario de Automática e Informática Industrial, Universitat Politècnica de València, Valencia, Spain

    Antonio Sala

  3. Department of Automation, Technical University of Cluj-Napoca, Cluj-Napoca, Romania

    Zsófia Lendek

  4. Department of Automation and Control, LAMI HUMR CNRS8201, Université Polytechnique Hauts-de-France, Valenciennes, France

    Thierry Marie Guerra

Authors
  1. Miguel Bernal
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  2. Antonio Sala
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  3. Zsófia Lendek
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  4. Thierry Marie Guerra
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Corresponding author

Correspondence to Miguel Bernal .

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Bernal, M., Sala, A., Lendek, Z., Guerra, T.M. (2022). State Feedback, Performance, and Robustness. In: Analysis and Synthesis of Nonlinear Control Systems. Studies in Systems, Decision and Control, vol 408. Springer, Cham. https://doi.org/10.1007/978-3-030-90773-0_5

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  • DOI: https://doi.org/10.1007/978-3-030-90773-0_5

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