Skip to main content
SpringerLink
Log in

On the Role of Zeros in the Pole Assignment of Scalar High-Order Fully Actuated Linear Systems

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

It is well known that for a linear system in state space form, controllability is equivalent to arbitrary pole assignment by state feedback. This brief points out that for a scalar high-order fully actuated linear system, the pole assignment problem is solvable if and only if the desired pole set of the closed-loop system should not include the zero set of the open-loop system if the implementation issue of the controller is taken into account, that is, controllability cannot guarantee arbitrary pole assignment by state feedback.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Kailath T, Linear Systems, Englewood Cliffs, Prentice-Hall, NJ, Upper Saddle River, 1980.

    MATH  Google Scholar 

  2. Duan G R, High-order fully actuated system approaches: Part I. Models and basic procedure, International Journal of System Sciences, 2021, 52(2): 422–435.

    Article  MathSciNet  Google Scholar 

  3. Duan G R and Zhou B, Fully actuated system approach for linear systems control: A frequency-domain solution, Journal of Systems Science & Complexity, 2022, 35(2).

  4. Kalman R E, Falb P L, and Arbib M A, Topics in Mathematical System Theory, McGraw-Hill, New York, 1969.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin, 150001, China

    Bin Zhou & Guang-Ren Duan

  2. Center for Control Science and Technology, Southern University of Science and Technology, Shenzhen, 518055, China

    Guang-Ren Duan

Authors
  1. Bin Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Guang-Ren Duan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Guang-Ren Duan.

Additional information

This paper was supported by the National Science Fund for Distinguished Young Scholars under Grant No. 62125303, and the Science Center Program of National Natural Science Foundation of China under Grant No. 62188101.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhou, B., Duan, GR. On the Role of Zeros in the Pole Assignment of Scalar High-Order Fully Actuated Linear Systems. J Syst Sci Complex 35, 535–542 (2022). https://doi.org/10.1007/s11424-022-2040-5

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-022-2040-5

Keywords

Search

Navigation