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Stability properties of coupled impedance passive LTI systems

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Zhao, Xiaowei and Weiss, George (2017) Stability properties of coupled impedance passive LTI systems. IEEE Transactions on Automatic Control, 62 (11). 5769 -5779. doi:10.1109/TAC.2017.2694558

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Official URL: http://dx.doi.org/10.1109/TAC.2017.2694558

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Abstract

We study the stability of the feedback interconnection
of two impedance passive linear time-invariant systems,
of which one is finite-dimensional. The closed-loop system is well known to be impedance passive, but no stability properties follow from this alone. We are interested in two main issues: (1)
the strong stability of the operator semigroup associated with the closed-loop system, (2) the input-output stability (meaning transfer function in H∞) of the closed-loop system. Our results are illustrated with the system obtained from the non-uniform SCOLE (NASA Spacecraft Control Laboratory Experiment) model representing a vertical beam clamped at the bottom, with a rigid body having a large mass on top, connected with a trolley
mounted on top of the rigid body, via a spring and a damper. Such an arrangement called a tuned mass damper (TMD), is used to stabilize tall buildings. We show that the SCOLE-TMD system is strongly stable on the energy state space and that the system is input-output stable from the horizontal force input to the horizontal velocity output.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
T Technology > TA Engineering (General). Civil engineering (General)
T Technology > TH Building construction
Divisions: Faculty of Science, Engineering and Medicine > Engineering > Engineering
Library of Congress Subject Headings (LCSH): Linear time invariant systems, Tuned mass dampers, Input-output analysis, Coupled mode theory, Linear systems, Stability
Journal or Publication Title: IEEE Transactions on Automatic Control
Publisher: IEEE
ISSN: 0018-9286
Official Date: November 2017
Dates:
DateEvent
November 2017Published
28 April 2017Available
29 March 2017Accepted
Volume: 62
Number: 11
Page Range: 5769 -5779
DOI: 10.1109/TAC.2017.2694558
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Funder: Israel Science Foundation (ISF), Leverhulme Trust (LT)
Grant number: 800/14 (ISF)
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