Jun Zheng and Guchuan Zhu
Article (2019)
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Accepted Version Terms of Use: All rights reserved. Download (428kB) |
Cite this document: | Zheng, J. & Zhu, G. (2019). A De Giorgi Iteration-based Approach for the Establishment of ISS Properties for Burgers' Equation with Boundary and In-domain Disturbances. IEEE Transactions on Automatic Control, 64(8). doi:10.1109/tac.2018.2880160 |
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Abstract
This note addresses input-to-state stability (ISS) properties with respect to (w.r.t.) boundary and in-domain disturbances for Burgers’ equation. The developed approach is a combination of the method of De Giorgi iteration and the technique of Lyapunov functionals by adequately splitting the original problem into two subsystems. The ISS properties in L2-norm for Burgers’ equation have been established using this method. Moreover, as an application of De Giorgi iteration, ISS in L1-norm w.r.t. in-domain disturbances and actuation errors in boundary feedback control for a 1-D linear unstable reaction-diffusion equation have also been established. It is the first time that the method of De Giorgi iteration is introduced in the ISS theory for infinite dimensional systems, and the developed method can be generalized for tackling some problems on multidimensional spatial domains and to a wider class of nonlinear partial differential equations (PDEs).
Uncontrolled Keywords
De Giorgi iteration, boundary disturbance, indomain disturbance, Burgers’ equation, unstable reaction-diffusion equation.
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Subjects: | 2500 Génie électrique et électronique > 2500 Génie électrique et électronique |
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Department: | Département de génie électrique |
Research Center: | Non applicable |
Funders: | CRSNG / NSERC |
Grant number: | RGPIN-2018-04571 |
Date Deposited: | 15 Jan 2019 12:09 |
Last Modified: | 08 Apr 2021 10:42 |
PolyPublie URL: | https://publications.polymtl.ca/3747/ |
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Journal Title: | IEEE Transactions on Automatic Control (vol. 64, no. 8) |
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Publisher: | IEEE |
Official URL: | https://doi.org/10.1109/tac.2018.2880160 |
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