Universal Method of Static Output Feedback Pole Placement for Fourth-Order Linear Time-Invariant Systems with Two Inputs and Two Outputs
A universal analytical method of static output feedback pole placement (for constructing controllers by output) for fourth-order linear time-invariant systems with two control inputs and two observable outputs is proposed, which does not depend on the relations between the controllability and observ...
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| Vydáno v: | Journal of computer & systems sciences international Ročník 64; číslo 2; s. 153 - 168 |
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| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Moscow
Pleiades Publishing
01.04.2025
Springer Nature B.V |
| Témata: | |
| ISSN: | 1064-2307, 1555-6530 |
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| Abstract | A universal analytical method of static output feedback pole placement (for constructing controllers by output) for fourth-order linear time-invariant systems with two control inputs and two observable outputs is proposed, which does not depend on the relations between the controllability and observability indices. The method does not require decomposing or reducing the system and may be applied to any fourth-order systems modally controllable by static output feedback, including systems irreducible to control (observation) with a single input (output). The method is based on linear matrix dependence of the characteristic polynomial of a closed-loop control system on the coefficients and determinant of a matrix of controller by output. The proposed approach gives the necessary and sufficient condition for static output feedback pole placement—it allows defining all possible matrices of controllers by output and the conditions of their existence. A new algebraic criterion of complete modal controllability by output is formulated and proved. Examples of applying the approach to controlling the aviation and space systems based on linearized models both in numerical and symbolic form are given. |
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| AbstractList | A universal analytical method of static output feedback pole placement (for constructing controllers by output) for fourth-order linear time-invariant systems with two control inputs and two observable outputs is proposed, which does not depend on the relations between the controllability and observability indices. The method does not require decomposing or reducing the system and may be applied to any fourth-order systems modally controllable by static output feedback, including systems irreducible to control (observation) with a single input (output). The method is based on linear matrix dependence of the characteristic polynomial of a closed-loop control system on the coefficients and determinant of a matrix of controller by output. The proposed approach gives the necessary and sufficient condition for static output feedback pole placement—it allows defining all possible matrices of controllers by output and the conditions of their existence. A new algebraic criterion of complete modal controllability by output is formulated and proved. Examples of applying the approach to controlling the aviation and space systems based on linearized models both in numerical and symbolic form are given. A universal analytical method of static output feedback pole placement (for constructing controllers by output) for fourth-order linear time-invariant systems with two control inputs and two observable outputs is proposed, which does not depend on the relations between the controllability and observability indices. The method does not require decomposing or reducing the system and may be applied to any fourth-order systems modally controllable by static output feedback, including systems irreducible to control (observation) with a single input (output). The method is based on linear matrix dependence of the characteristic polynomial of a closed-loop control system on the coefficients and determinant of a matrix of controller by output. The proposed approach gives the necessary and sufficient condition for static output feedback pole placement—it allows defining all possible matrices of controllers by output and the conditions of their existence. A new algebraic criterion of complete modal controllability by output is formulated and proved. Examples of applying the approach to controlling the aviation and space systems based on linearized models both in numerical and symbolic form are given. |
| Author | Lapin, A. V. Zubov, N. E. |
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| Cites_doi | 10.3103/S1068799820030319 10.3103/S1068799815030034 10.1134/S1064230724700424 10.1134/S1064230723010124 10.1109/TSCZh58792.2023.10233429 10.18698/1812-3368-2020-2-41-64 10.1134/S1064562417050179 10.1109/CoDIT49905.2020.9263844 10.1134/S1064230723020193 10.3103/S1068799819030073 10.1134/S1064230713030179 10.1109/JACC.1965.4168784 10.1134/S1064230717050033 10.3103/S106879981701010X 10.1109/RusAutoCon49822.2020.9208159 10.1016/0167-6911(88)90072-2 10.18698/1812-3368-2023-4-18-38 |
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| Copyright | Pleiades Publishing, Ltd. 2025 ISSN 1064-2307, Journal of Computer and Systems Sciences International, 2025, Vol. 64, No. 2, pp. 153–168. © Pleiades Publishing, Ltd., 2025. Pleiades Publishing, Ltd. 2025. |
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| Keywords | modal output control observability index trace of matrix controllability index complete modal controllability by output static output feedback pole placement one-sided matrix equation fourth-order control system |
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| References | 7505_CR4 N. E. Zubov (7505_CR5) 2017; 96 7505_CR7 7505_CR14 7505_CR8 7505_CR15 J. W. Van der Woude (7505_CR6) 1988; 11 N. E. Zubov (7505_CR13) 2019; 62 N. E. Zubov (7505_CR9) 2023; 62 N. E. Zubov (7505_CR12) 2013; 52 N. E. Zubov (7505_CR11) 2024; 63 S. Yu. Zheltov (7505_CR16) 2021 R. W. Bass (7505_CR18) 1965; 3 N. E. Zubov (7505_CR1) 2015; 58 N. E. Zubov (7505_CR3) 2017; 60 N. Yu. Borisenko (7505_CR20) 2017; 56 7505_CR17 N. E. Zubov (7505_CR10) 2023; 62 7505_CR19 N. E. Zubov (7505_CR2) 2020; 63 |
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| SubjectTerms | Closed loops Control Control in Deterministic Systems Control systems Controllability Controllers Decomposition Determinants Engineering Feedback control Mechatronics Observability (systems) Output feedback Pole placement Polynomials Robotics Time invariant systems |
| Title | Universal Method of Static Output Feedback Pole Placement for Fourth-Order Linear Time-Invariant Systems with Two Inputs and Two Outputs |
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