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

doi:10.1007/s11424-022-2040-5

Journal of Systems Science and Complexity ›› 2022, Vol. 35 ›› Issue (2): 535-542.DOI: 10.1007/s11424-022-2040-5

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

ZHOU Bin¹, DUAN Guang-Ren^1,2

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.

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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.

Key words: High-order fully actuated systems, pole assignment, state feedback, zeros

[1] Kailath T, Linear Systems, Englewood Cliffs, Prentice-Hall, NJ, Upper Saddle River, 1980.
[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.
[3] Duan G R and Zhou B, Fully actuated system approach for linear systems control: A frequencydomain 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.

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[2]	CHAI Lin , QIAN Chunjiang. STATE FEEDBACK STABILIZATION FOR A CLASS OF NONLINEAR TIME-DELAY SYSTEMS VIA DYNAMIC LINEAR CONTROLLERS [J]. Journal of Systems Science and Complexity, 2014, 27(3): 453-462.
[3]	Zhaoqiang GE;Guangtian ZHU;Dexing FENG. ON STATE FEEDBACK AND POLE ASSIGNMENT OF THE SECOND ORDER COUPLED SINGULAR DISTRIBUTED PARAMETER SYSTEMS IN HILBERT SPACE [J]. Journal of Systems Science and Complexity, 2011, 24(3): 457-465.
[4]	Xi Liu;Qingling Zhang;Lichun Zhao. Stabilization of a Kind of Prey-Predator Model with Holling Functional Response [J]. Journal of Systems Science and Complexity, 2006, 19(3): 436-440.
[5]	Shi He. THE POLE ASSIGNMENT OF LINEAR SYSTEMS [J]. Journal of Systems Science and Complexity, 1991, 4(4): 349-361.

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