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Controller Design for Continuous-Time Linear Control Systems with Time-Varying Delay

Author

Listed:
  • Hongli Yang

    (College of Information Science and Technology, Qingdao Huanghai University, Linghai Road 1145, Qingdao 266427, China)

  • Lijuan Yang

    (College of Mathematics and Systems Science, Shandong University of Science and Technology, Qianwangang Road 579, Qingdao 266590, China)

  • Ivan Ganchev Ivanov

    (Faculty of Economics and Business Administration, Sofia University “St. Kl. Ohridski”, 1000 Sofia, Bulgaria)

Abstract

This paper addresses the controller design problem for linear systems with time-varying delays. By constructing a novel Lyapunov–Krasovskii functional incorporating delay-partitioning techniques, we establish delay-dependent stability criteria for the solvability of the robust stabilization problem. The derived conditions are formulated as linear matrix inequalities (LMIs) that become affine upon fixing a single scalar parameter, thereby facilitating efficient numerical computation. Furthermore, these criteria guarantee that the reachable set of the closed-loop system remains bounded within a prescribed ellipsoid under zero initial conditions. The effectiveness and superiority of the proposed approach are demonstrated through two comparative numerical examples, including a benchmark problem with varying delay.

Suggested Citation

  • Hongli Yang & Lijuan Yang & Ivan Ganchev Ivanov, 2025. "Controller Design for Continuous-Time Linear Control Systems with Time-Varying Delay," Mathematics, MDPI, vol. 13(15), pages 1-11, August.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:15:p:2519-:d:1718194
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    References listed on IDEAS

    as
    1. Dong-Hoon Lee & Yeong-Jae Kim & Seung-Hoon Lee & Oh-Min Kwon, 2024. "Enhancing Stability Criteria for Linear Systems with Interval Time-Varying Delays via an Augmented Lyapunov–Krasovskii Functional," Mathematics, MDPI, vol. 12(14), pages 1-19, July.
    2. 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.
    3. 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.
    Full references (including those not matched with items on IDEAS)

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