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Peak-to-Peak Stabilization of Sampled-Data Systems Subject to Actuator Saturation and Its Practical Application to an Inverted Pendulum

Author

Listed:
  • Khanh Hieu Nguyen

    (Department of Electrical, Electronic and Computer Engineering, University of Ulsan, Daehak-ro 93, Nam-gu, Ulsan 680-749, Republic of Korea)

  • Sung Hyun Kim

    (Department of Electrical, Electronic and Computer Engineering, University of Ulsan, Daehak-ro 93, Nam-gu, Ulsan 680-749, Republic of Korea)

Abstract

This paper investigates the local stability and stabilization criteria of sampled-data control systems, taking into account actuator saturation and peak-bounded exogenous disturbances. Specifically, this study introduces two innovations to extend the maximum upper bound of the sampling interval: two novel time integrals of the weighted state derivative are introduced to formulate an improved looped-functional; second, the introduction of two supplementary zero-equalities to improve the relationship among the components of the augmented state. Building on this, a set of linear matrix inequality-based stabilization conditions is derived. These conditions ensure that a closed-loop sampled-data system can become exponentially stable and achieve a guaranteed peak-to-peak performance in the domain of attraction. Finally, the efficacy of the proposed methodology is substantiated through both simulation and experimental results, focusing on the sampled-data control of an inverted pendulum system.

Suggested Citation

  • Khanh Hieu Nguyen & Sung Hyun Kim, 2023. "Peak-to-Peak Stabilization of Sampled-Data Systems Subject to Actuator Saturation and Its Practical Application to an Inverted Pendulum," Mathematics, MDPI, vol. 11(22), pages 1-19, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:22:p:4592-:d:1277083
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    References listed on IDEAS

    as
    1. Khanh Hieu Nguyen & Sung Hyun Kim, 2022. "Event-Triggered Non-PDC Filter Design of Fuzzy Markovian Jump Systems under Mismatch Phenomena," Mathematics, MDPI, vol. 10(16), pages 1-25, August.
    2. Nguyen, Khanh Hieu & Kim, Sung Hyun, 2024. "Improved stability and stabilization criteria of sampled-data control systems based on an enhanced looped-functional," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 69-81.
    3. Nguyen, Khanh Hieu & Kim, Sung Hyun, 2022. "Improved sampled-data control design of T-S fuzzy systems against mismatched fuzzy-basis functions," Applied Mathematics and Computation, Elsevier, vol. 428(C).
    4. Omer Saleem & Faisal Abbas & Jamshed Iqbal, 2023. "Complex Fractional-Order LQIR for Inverted-Pendulum-Type Robotic Mechanisms: Design and Experimental Validation," Mathematics, MDPI, vol. 11(4), pages 1-21, February.
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