Selivanov, A. orcid.org/0000-0001-5075-7229 and Fridman, E. (2019) Delayed H∞ control of 2D diffusion systems under delayed pointlike measurements. Automatica, 109. 108541. ISSN 0005-1098
Abstract
Up to now, robust control of multi-dimensional diffusion systems was confined to averaged measurements. In this paper, we consider 2D diffusion systems with delayed pointlike measurements. A pointlike measurement is the state value averaged over a small subdomain that approximates its point value. The main novelty enabling the study of such measurements is a new inequality, which we call the reciprocally convex variation of Friedrich’s inequality. It bounds the difference between a function and its point values in the L2-norm using the function’s derivatives. Combining this result with a new Lyapunov–Krasovskii functional, which has a spatially-varying kernel, we solve the H∞ control and filtering problems in the presence of time-varying input and output delays. We show that any 2D semilinear diffusion system with pointlike measurements can be stabilized by static output feedback applied through characteristic functions if the controller gain and number of sensors/actuators are large enough while the input and output delays are sufficiently small. The results are demonstrated on a 2D catalytic slab model.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2019 Elsevier Ltd. This is an author produced version of a paper subsequently published in Automatica. Uploaded in accordance with the publisher's self-archiving policy. Article available under the terms of the CC-BY-NC-ND licence (https://creativecommons.org/licenses/by-nc-nd/4.0/). |
Keywords: | Distributed parameter systems; Time-delays; Lyapunov–Krasovskii functionals; LMIs |
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 10:45 |
Last Modified: | 23 Aug 2020 00:38 |
Status: | Published |
Publisher: | Elsevier BV |
Refereed: | Yes |
Identification Number: | 10.1016/j.automatica.2019.108541 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:153371 |