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Output Stabilization of Linear Systems in Given Set

Author

Listed:
  • Ba Huy Nguyen

    (Adaptive and Intelligent Control of Network and Distributed Systems Laboratory, Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences (IPME RAS), 199178 Saint-Petersburg, Russia
    Faculty of Control Systems and Robotics, ITMO University, 197101 Saint-Petersburg, Russia
    These authors contributed equally to this work.)

  • Igor B. Furtat

    (Adaptive and Intelligent Control of Network and Distributed Systems Laboratory, Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences (IPME RAS), 199178 Saint-Petersburg, Russia
    These authors contributed equally to this work.)

Abstract

This paper presents a method for designing control laws to achieve output stabilization of linear systems within specified sets, even in the presence of unknown bounded disturbances. The approach consists of two stages. In the first stage, a coordinate transformation is utilized to convert the original system with output constraints into a new system without constraints. In the second stage, a controller is designed to ensure the boundedness of the controlled variable of the transformed system obtained in the first stage. Two distinct control strategies are presented in the second stage, depending on the measurability of the state vector. If the state vector is measurable, a controller is designed using state feedback based on the Lyapunov method and Linear Matrix Inequalities (LMIs). Alternatively, if only the output vector is measurable, an observer-based controller is designed using a Luenberger observer. In this case, the state estimation error does not need to converge to zero but must remain bounded. The efficacy of the proposed method and the validity of the theoretical results are demonstrated through simulations performed in MATLAB/Simulink.

Suggested Citation

  • Ba Huy Nguyen & Igor B. Furtat, 2023. "Output Stabilization of Linear Systems in Given Set," Mathematics, MDPI, vol. 11(16), pages 1-16, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3542-:d:1218509
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    References listed on IDEAS

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    1. Fazilah Hassan & Argyrios Zolotas & George Halikias, 2023. "New Insights on Robust Control of Tilting Trains with Combined Uncertainty and Performance Constraints," Mathematics, MDPI, vol. 11(14), pages 1-19, July.
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