@inproceedings{392d6a8dc1114dcda7cc33de411ca90a,
title = "Enforcing a system model to be negative imaginary via perturbation of Hamiltonian matrices",
abstract = "Flexible structure dynamics with collocated force actuators and position sensors lead to negative imaginary (NI) systems. However, in some cases, the models obtained for these systems may not satisfy the NI property. This paper provides a new method for enforcing such models to be NI. The results are based on a study of the spectral properties of related Hamiltonian matrices. A test for the negativity of the imaginary part of a corresponding transfer function matrix is first performed by checking for the existence of imaginary eigenvalues of the associated Hamiltonian matrix. In the presence of imaginary eigenvalues, the system is not NI. In such cases, a first-order perturbation is presented for the precise characterization of frequency bands where violations of the NI property occur. This characterization is then used for the design of an iterative perturbation scheme for state matrices aimed at displacing the imaginary eigenvalues of the Hamiltonian matrix away from the imaginary axis.",
keywords = "Hamiltonian matrices, Negative imaginary systems, Passivity, Positive real systems",
author = "Mabrok, \{Mohamed A.\} and Kallapur, \{Abhijit G.\} and Petersen, \{Ian R.\} and Alexander Lanzon",
year = "2011",
doi = "10.1109/CDC.2011.6160286",
language = "English",
isbn = "9781612848006",
series = "Proceedings of the IEEE Conference on Decision and Control",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "3748--3752",
booktitle = "2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011",
address = "United States",
note = "2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 ; Conference date: 12-12-2011 Through 15-12-2011",
}