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

ZHOU Bin1, DUAN Guang-Ren1,2

1. 1. Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin 150001, China;
2. Center for Control Science and Technology, Southern University of Science and Technology, Shenzhen 518055, China
• Received:2022-01-15 Published:2022-04-13
• Supported by:
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.

ZHOU Bin, DUAN Guang-Ren. On the Role of Zeros in the Pole Assignment of Scalar High-Order Fully Actuated Linear Systems[J]. Journal of Systems Science and Complexity, 2022, 35(2): 535-542.

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.
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