Selivanov, A. orcid.org/0000-0001-5075-7229 and Fridman, E. (2019) Boundary observers for a reaction–diffusion system under time-delayed and sampled-data measurements. IEEE Transactions on Automatic Control, 64 (8). pp. 3385-3390. ISSN 0018-9286
Abstract
We construct finite-dimensional observers for a one-dimensional reaction-diffusion system with boundary measurements subject to time-delays and data sampling. The system has a finite number of unstable modes approximated by a Luenberger-type observer. The remaining modes vanish exponentially. For a given reaction coefficient, we show how many modes one should use to achieve a desired rate of convergence. The finite-dimensional part is analyzed using appropriate Lyapunov-Krasovskii functionals that lead to linear matrix inequalitie (LMI)-based convergence conditions feasible for small enough time-delay and sampling period. The LMIs can be used to find appropriate injection gains.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. Reproduced in accordance with the publisher's self-archiving policy. |
Keywords: | Boundary measurements; data sampling; observers; partial differential equations; time-delays |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Automatic Control and Systems Engineering (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 12 Nov 2019 14:14 |
Last Modified: | 12 Nov 2019 14:22 |
Status: | Published |
Publisher: | Institute of Electrical and Electronics Engineers (IEEE) |
Refereed: | Yes |
Identification Number: | 10.1109/tac.2018.2877381 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:153372 |