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.
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References
Kailath T, Linear Systems, Englewood Cliffs, Prentice-Hall, NJ, Upper Saddle River, 1980.
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.
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).
Kalman R E, Falb P L, and Arbib M A, Topics in Mathematical System Theory, McGraw-Hill, New York, 1969.
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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.
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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
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DOI: https://doi.org/10.1007/s11424-022-2040-5