Jun Zheng, Guchuan Zhu and Sergey Dashkovskiy
Article (2022)
|
Open Access to the full text of this document Accepted Version Terms of Use: All rights reserved Download (344kB) |
Abstract
In this paper, we introduce the notion of relative K-equi-stability (RKES) to characterize the uniformly continuous dependence of (weak) solutions on external disturbances for nonlinear parabolic PDE systems. Based on the RKES, we prove the input-to-state stability (ISS) in the spatial sup-norm for a class of nonlinear parabolic PDEs with either Dirichlet or Robin boundary disturbances. An example concerned with a super-linear parabolic PDE with Robin boundary condition is provided to illustrate the obtained ISS results. Besides, as an application of the notion of RKES, we conduct stability analysis for a class of parabolic PDEs in cascade coupled over the domain or on the boundary of the domain, in the spatial and time sup-norm, and in the spatial sup-norm, respectively. The technique of De Giorgi iteration is extensively used in the proof of the results presented in this paper.
Uncontrolled Keywords
Subjects: | 2500 Electrical and electronic engineering > 2500 Electrical and electronic engineering |
---|---|
Department: | Department of Electrical Engineering |
Funders: | NSFC, CRSNG/NSERC, German Research Foundation (DFG) |
Grant number: | 11901482, RGPIN-2018-04571, DA 767/12-1 |
PolyPublie URL: | https://publications.polymtl.ca/10400/ |
Journal Title: | IEEE Transactions on Automatic Control (vol. 67, no. 10) |
Publisher: | IEEE |
DOI: | 10.1109/tac.2022.3192325 |
Official URL: | https://doi.org/10.1109/tac.2022.3192325 |
Date Deposited: | 27 Jul 2022 13:53 |
Last Modified: | 07 Apr 2025 23:04 |
Cite in APA 7: | Zheng, J., Zhu, G., & Dashkovskiy, S. (2022). Relative stability in the sup-norm and input-to-state stability in the spatial sup-norm for parabolic PDEs. IEEE Transactions on Automatic Control, 67(10), 5361-5375. https://doi.org/10.1109/tac.2022.3192325 |
---|---|
Statistics
Total downloads
Downloads per month in the last year
Origin of downloads
Dimensions