Article Contents

2019, Volume 2, Issue 3: 251-266. Doi: 10.3934/mfc.2019016

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Eigenstructure assignment for polynomial matrix systems ensuring normalization and impulse elimination

Peizhao Yu^1, , and
Guoshan Zhang^2,

1.
School of Electrical and Information Engineering, Zhengzhou University of Light Industry, Zhengzhou 450002, China
2.
School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, China

^* Corresponding author: Peizhao Yu
^* Corresponding author: Peizhao Yu

Received: May 2019

Revised: July 2019

Published: September 2019

The first author is supported by the National Natural Science Foundation of China grant 61903342 and the Doctor fund project of Zhengzhou University of Light Industry grant 2017BSJJ009; The second author is supported by the National Natural Science Foundation of China grant 61473202.

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Abstract

In this paper, eigenstructure assignment problems for polynomial matrix systems ensuring normalization and impulse elimination are considered. By using linearization method, a polynomial matrix system is transformed into a descriptor linear system without changing the eigenstructure of original system. By analyzing the characteristic polynomial of the desired system, the normalizable condition under feedback is given, and moreover, the parametric expressions of controller gains for eigenstructure ensuring normalization are derived by singular value decomposition. Impulse elimination in polynomial matrix systems is investigated when the normalizable condition is not satisfied. The parametric expressions of controller gains for impulse elimination ensuring finite eigenstructure assignment are formulated. The solving algorithms of corresponding controller gains for eigenstructure assignment ensuring normalization and impulse elimination are also presented. Numerical examples show the effectiveness of proposed method.

Keywords:

Mathematics Subject Classification: Primary: 15A18, 93B18; Secondary: 93C05.

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Figure 1. The responses of $ x $ and $ \dot{x} $ for normalization

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Figure 2. The responses of $ x $ and $ \dot{x} $ for impulse elimination

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Figure 3. The responses of $ {x} $ and $ \dot{x} $ for impulse elimination

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Figure 4. The responses of $ \ddot{x} $ and $ x^{(3)} $ for impulse elimination

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