TY - GEN
T1 - Enforcing a system model to be negative imaginary via perturbation of Hamiltonian matrices
AU - Mabrok, Mohamed A.
AU - Kallapur, Abhijit G.
AU - Petersen, Ian R.
AU - Lanzon, Alexander
PY - 2011
Y1 - 2011
N2 - 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.
AB - 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.
KW - Hamiltonian matrices
KW - Negative imaginary systems
KW - Passivity
KW - Positive real systems
UR - http://www.scopus.com/inward/record.url?scp=84860699350&partnerID=8YFLogxK
U2 - 10.1109/CDC.2011.6160286
DO - 10.1109/CDC.2011.6160286
M3 - Conference contribution
SN - 9781612848006
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 3748
EP - 3752
BT - 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Y2 - 12 December 2011 through 15 December 2011
ER -