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Robust Invariance Conditions of Uncertain Linear Discrete Time Systems Based on Semidefinite Programming Duality

Author

Listed:
  • Hongli Yang

    (College of Big Data, Qingdao Huanghai University, Linghai Road 1145, Qingdao 266427, China
    These authors contributed equally to this work.)

  • Chengdan Wang

    (College of Mathematics and Systems Science, Shandong University of Science and Technology, Qianwangang Road 579, Qingdao 266590, China
    These authors contributed equally to this work.)

  • Xiao Bi

    (School of Mathematics, Shandong University, Jinan 250100, China
    These authors contributed equally to this work.)

  • Ivan Ganchev Ivanov

    (Faculty of Economics and Business Administration, Sofia University “St. Kl. Ohridski”, 1000 Sofia, Bulgaria
    These authors contributed equally to this work.)

Abstract

This article proposes a novel robust invariance condition for uncertain linear discrete-time systems with state and control constraints, utilizing a method of semidefinite programming duality. The approach involves approximating the robust invariant set for these systems by tackling the dual problem associated with semidefinite programming. Central to this method is the formulation of a dual programming through the application of adjoint mapping. From the standpoint of semidefinite programming dual optimization, the paper presents a novel linear matrix inequality (LMI) conditions pertinent to robust positive invariance. Illustrative examples are incorporated to elucidate the findings.

Suggested Citation

  • Hongli Yang & Chengdan Wang & Xiao Bi & Ivan Ganchev Ivanov, 2024. "Robust Invariance Conditions of Uncertain Linear Discrete Time Systems Based on Semidefinite Programming Duality," Mathematics, MDPI, vol. 12(16), pages 1-14, August.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:16:p:2512-:d:1456280
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    References listed on IDEAS

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    1. Chengdan Wang & Hongli Yang & Ivan Ganchev Ivanov, 2023. "Controlled Invariant Sets of Discrete-Time Linear Systems with Bounded Disturbances," Mathematics, MDPI, vol. 11(15), pages 1-16, August.
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