NDLI: Enforcing a system model to be negative imaginary via perturbation of Hamiltonian matrices

Content Provider	IEEE Xplore Digital Library
Author	Mabrok, M.A. Kallapur, A.G. Petersen, I.R. Lanzon, A.
Copyright Year	2011
Description	Author affiliation: School of Engineering and Information Technology, University of New South Wales at the Australian Defence Force Academy Canberra ACT 2600, Australia (Mabrok, M.A.; Kallapur, A.G.; Petersen, I.R.) \|\| Control Systems Centre, School of Electrical and Electronic Engineering, University of Manchester, M13 9PL, United Kingdom (Lanzon, A.)
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.
Starting Page	3748
Ending Page	3752
File Size	205007
Page Count	5
File Format	PDF
ISBN	9781612848006
ISSN	07431546
e-ISBN	9781612848013
e-ISBN	9781612847993
DOI	10.1109/CDC.2011.6160286
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2011-12-12
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Nickel Eigenvalues and eigenfunctions Transfer functions Computed tomography Stability analysis Integrated circuit interconnections Control systems Passivity Negative imaginary systems Positive real systems Hamiltonian matrices
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Control and Systems Engineering Modeling and Simulation

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