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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
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 |
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| 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: |
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| 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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