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Stability Analysis and Synthesis for 2-D Switched Systems with Random Disturbance

Author

Listed:
  • Fei Meng

    (Department of System Science, University of Shanghai for Science and Technology, Shanghai 200093, China)

  • Xuyu Shen

    (Department of System Science, University of Shanghai for Science and Technology, Shanghai 200093, China)

  • Xiaofeng Li

    (Department of Information and Computing Science, Huaiyin Institute of Technology, Huai’an 223001, China)

Abstract

In this paper, the stability analysis and controller design of two-dimensional (2-D) switched system with random disturbances are studied. First, based on the Fornasini–Marchesini local state space model, a random discrete 2-D switched system model is proposed. Secondly, based on the method of switching quadratic Lyapunov function, Schur complement and linear matrix inequality the criterion of the sufficiency of the asymptotically stable under any switching signal is established. The extended average residence time method is used to obtain a sufficient criterion of the mean square exponential stability of the random discrete 2-D switched system under restricted switching conditions. According to the stability analysis results, the conditions for the existence of the state feedback controller are given and the corresponding state feedback controller is designed. Finally, two examples are given to illustrate the effectiveness of the proposed method.

Suggested Citation

  • Fei Meng & Xuyu Shen & Xiaofeng Li, 2022. "Stability Analysis and Synthesis for 2-D Switched Systems with Random Disturbance," Mathematics, MDPI, vol. 10(5), pages 1-18, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:5:p:810-:d:763441
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    References listed on IDEAS

    as
    1. Abdellah Benzaouia & Abdelaziz Hmamed & Fernando Tadeo & Ahmed EL Hajjaji, 2011. "Stabilisation of discrete 2D time switching systems by state feedback control," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(3), pages 479-487.
    2. Huiying Liu & Lijun Gao & Zhenyue Wang & Zihan Liu, 2021. "Asynchronous l2 – l∞ filtering of discrete-time impulsive switched systems with admissible edge-dependent average dwell time switching signal," International Journal of Systems Science, Taylor & Francis Journals, vol. 52(8), pages 1564-1585, June.
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    Cited by:

    1. Manuel De la Sen & Asier Ibeas, 2022. "On Some Properties of a Class of Eventually Locally Mixed Cyclic/Acyclic Multivalued Self-Mappings with Application Examples," Mathematics, MDPI, vol. 10(14), pages 1-29, July.

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