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Finite-Time Guaranteed Cost Control for Markovian Jump Systems with Time-Varying Delays

Author

Listed:
  • Xikui Liu

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

  • Wencong Li

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

  • Chenxin Yao

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

  • Yan Li

    (Department of Fundamental Courses, Shandong University of Science and Technology, Jinan 250031, China)

Abstract

In this paper, the finite-time guaranteed cost control (FTGCC) problem is addressed for Itô Markovian jump systems with time-varying delays. The aim of this paper is to design a state feedback guaranteed cost controller, such that not only the resulting closed-loop systems are finite-time stable, but also cost performance has a minimum upper bound. First, new sufficient conditions for the existence of guaranteed cost controllers are presented via the linear matrix inequality (LMI) approach. Then, based on the established conditions, the desired controllers are designed and the upper bound of cost performance is provided. In the end, an example is employed to show the validity of the obtained results.

Suggested Citation

  • Xikui Liu & Wencong Li & Chenxin Yao & Yan Li, 2022. "Finite-Time Guaranteed Cost Control for Markovian Jump Systems with Time-Varying Delays," Mathematics, MDPI, vol. 10(12), pages 1-12, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:12:p:2028-:d:836734
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    References listed on IDEAS

    as
    1. Wang, Guoliang & Li, Zhiqiang & Zhang, Qingling & Yang, Chunyu, 2017. "Robust finite-time stability and stabilization of uncertain Markovian jump systems with time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 377-393.
    2. Gholami, Hadi & Shafiei, Mohammad Hossein, 2021. "Finite-time H∞ static and dynamic output feedback control for a class of switched nonlinear time-delay systems," Applied Mathematics and Computation, Elsevier, vol. 389(C).
    3. Yan, Zhiguo & Song, Yunxia & Liu, Xiaoping, 2018. "Finite-time stability and stabilization for Itô-type stochastic Markovian jump systems with generally uncertain transition rates," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 512-525.
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    Cited by:

    1. Jianrong Chen & Xiangui Kang & Yunong Zhang, 2023. "Continuous and Discrete ZND Models with Aid of Eleven Instants for Complex QR Decomposition of Time-Varying Matrices," Mathematics, MDPI, vol. 11(15), pages 1-18, July.
    2. Aravindh Dharmarajan & Parivallal Arumugam & Sakthivel Ramalingam & Kavikumar Ramasamy, 2023. "Equivalent-Input-Disturbance Based Robust Control Design for Fuzzy Semi-Markovian Jump Systems via the Proportional-Integral Observer Approach," Mathematics, MDPI, vol. 11(11), pages 1-16, June.
    3. 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.
    4. Xinlan Guo & Mohammadamin Shirkhani & Emad M. Ahmed, 2022. "Machine-Learning-Based Improved Smith Predictive Control for MIMO Processes," Mathematics, MDPI, vol. 10(19), pages 1-19, October.

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