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Reachable Set Estimation and Controller Design for Linear Time-Delayed Control System with Disturbances

Author

Listed:
  • Yongchun Jiang

    (College of Big Data, Qingdao Huanghai University, Qingdao 266427, China)

  • Hongli Yang

    (College of Big Data, Qingdao Huanghai University, Qingdao 266427, China
    College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China)

  • Ivan Ganchev Ivanov

    (Faculty of Economics and Business Administration, Sofia University “St. Kl. Ohridski”, 125 Tzarigradsko Chaussee Blvd., Bl. 3, 1113 Sofia, Bulgaria)

Abstract

This paper investigates reachable set estimation and state-feedback controller design for linear time-delay control systems with bounded disturbances. By constructing an appropriate Lyapunov–Krasovskii functional, we obtain a delay-dependent condition, which determines the admissible bounding ellipsoid for the reachable set of the system we considered. Then, a sufficient condition in the form of liner matrix inequalities is given to solve the problem of controller design and reachable set estimation. Then, by minimizing the volume of the ellipsoid and solving the liner matrix inequality, we obtain the desired ellipsoid and controller gain. A comparative numerical example is given to show the effectiveness of our result.

Suggested Citation

  • Yongchun Jiang & Hongli Yang & Ivan Ganchev Ivanov, 2024. "Reachable Set Estimation and Controller Design for Linear Time-Delayed Control System with Disturbances," Mathematics, MDPI, vol. 12(2), pages 1-10, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:2:p:176-:d:1314017
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    References listed on IDEAS

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    1. C. Durieu & É. Walter & B. Polyak, 2001. "Multi-Input Multi-Output Ellipsoidal State Bounding," Journal of Optimization Theory and Applications, Springer, vol. 111(2), pages 273-303, November.
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