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Partial Eigenstructure Assignment for Linear Time-Invariant Systems via Dynamic Compensator

Author

Listed:
  • Da-Ke Gu

    (School of Automation Engineering, Northeast Electric Power University, Jilin 132012, China)

  • Zhi-Jing Guo

    (School of Automation Engineering, Northeast Electric Power University, Jilin 132012, China)

  • Rui-Yuan Wang

    (School of Automation Engineering, Northeast Electric Power University, Jilin 132012, China)

  • Yin-Dong Liu

    (School of Automation Engineering, Northeast Electric Power University, Jilin 132012, China)

Abstract

This article studies the partial eigenstructure assignment (PEA) problem for a type of linear time-invariant (LTI) system. By introducing a dynamic output feedback controller, the closed-loop system is similar to a given arbitrary constant matrix, so the desired closed-loop eigenstructure can be obtained. Different from the normal eigenstructure assignment, only a part of the left and right generalized eigenvectors is assigned to the closed-loop system to remove complicated constraints, which reflects the partial eigenstructure assignment. Meanwhile, based on the solutions to the generalized Sylvester equations (GSEs), two arbitrary parameter matrices representing the degrees of freedom are presented to obtain the parametric form of the coefficient matrices of the dynamic compensator and the partial eigenvector matrices. Finally, an illustrative example and the simulation results prove the excellent effectiveness and feasibility of parametric method we proposed.

Suggested Citation

  • Da-Ke Gu & Zhi-Jing Guo & Rui-Yuan Wang & Yin-Dong Liu, 2023. "Partial Eigenstructure Assignment for Linear Time-Invariant Systems via Dynamic Compensator," Mathematics, MDPI, vol. 11(13), pages 1-19, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:2866-:d:1179777
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    References listed on IDEAS

    as
    1. A. Baddou & H. Maarouf & A. Benzaouia, 2013. "Partial eigenstructure assignment problem and its application to the constrained linear problem," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(5), pages 908-915.
    2. Gu, Da-Ke & Zhang, Da-Wei, 2020. "Parametric control to second-order linear time-varying systems based on dynamic compensator and multi-objective optimization," Applied Mathematics and Computation, Elsevier, vol. 365(C).
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