A robust regional eigenvalue assignment problem using rank-one control for undamped gyroscopic systems

• Published in: AIMS mathematics Vol. 9; no. 7; pp. 19104 - 19124
• Main Authors: He, Binxin, Liu, Hao
• Format: Journal Article
• Language: English
• Published: AIMS Press 01.01.2024
• Subjects: rank-one control; regional eigenvalue assignment; robustness; undamped gyroscopic systems
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.2024931

Considering the advantages of economic benefit and cost reduction by using rank-one control, we investigated the problem of robust regional eigenvalue assignment using rank-one control for undamped gyroscopic systems. Based on the orthogonality relation, we presented a method for solving partial eigenvalue assignment problems to reassign partial undesired eigenvalues accurately. Since it is difficult to achieve robust control by assigning desired eigenvalues to precise positions with rank-one control, we assigned eigenvalues within specified regions to provide the necessary freedom. According to the sensitivity analysis theories, we derived the sensitivity of closed-loop eigenvalues to parameter perturbations to measure robustness and proposed a numerical algorithm for solving robust regional eigenvalue assignment problems so that the closed-loop eigenvalues were insensitive to parameter perturbations. Numerical experiments demonstrated the effectiveness of our method.