A parametric approach of partial eigenstructure assignment for high-order linear systems via proportional plus derivative state feedback

• Main Authors: Da-Ke Gu, Rui-Yuan Wang, Yin-Dong Liu
• Format: Article
• Language: English
• Published: AIMS Press 2021-08-01
• Series: AIMS Mathematics
• Subjects: partial eigenstructure assignment; high-order lti systems; parametric approach; high-order generalized sylvester equations (hgse); pd state feedback
• Online Access: https://www.aimspress.com/article/doi/10.3934/math.2021647?viewType=HTML

In this paper, a partial eigenstructure assignment problem for the high-order linear time-invariant (LTI) systems via proportional plus derivative (PD) state feedback is considered. By partitioning the open-loop system into two parts (the altered part and the unchanged part) and utilizing the solutions to the high-order generalized Sylvester equation (HGSE), complete parametric expressions of the feedback gain matrices of the closed-loop system are established. Meanwhile, a group of arbitrary parameters representing the degrees of freedom of the proposed method is provided and optimized to satisfy the stability of the system and robustness criteria. Finally, a numerical example and a three-axis dynamic flight motion simulator system example with the simulation results are offered to illustrate the effectiveness and superiority of the proposed method.