<  Back to the Polytechnique Montréal portal

A De Giorgi Iteration-based Approach for the Establishment of ISS Properties for Burgers' Equation with Boundary and In-domain Disturbances

Jun Zheng and Guchuan Zhu

Article (2019)

[img]
Preview
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. doi:10.1109/tac.2018.2880160
Show abstract Hide abstract

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.

Open Access document in PolyPublie
Subjects: 2500 Génie électrique et électronique > 2500 Génie électrique et électronique
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: 04 Jul 2019 16:04
PolyPublie URL: https://publications.polymtl.ca/3747/
Document issued by the official publisher
Journal Title: IEEE Transactions on Automatic Control
Publisher: IEEE
Official URL: https://doi.org/10.1109/tac.2018.2880160

Statistics

Total downloads

Downloads per month in the last year

Origin of downloads

Dimensions

Repository Staff Only