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Finite-dimensional output stabilization of linear diffusion-reaction systems : a small-gain approach

Title data

Grüne, Lars ; Meurer, Thomas:
Finite-dimensional output stabilization of linear diffusion-reaction systems : a small-gain approach.
Bayreuth ; Kiel , 2021 . - 13 p.

Official URL: Volltext

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Project information

Project title:
Project's official titleProject's id
Model predictive PDE control for energy efficient building operation: Economic model predictive control and time varying systemsGR 1569/16-1

Project financing: Deutsche Forschungsgemeinschaft

Abstract in another language

A small-gain approach is proposed to analyze closed-loop stability of linear diffusion-reaction systems under finite-dimensional observer-based state feedback control. For this, the decomposition of the infinite-dimensional system into a finite-dimensional slow subsystem used for design and an infinite-dimensional residual fast subsystem is considered. The effect of observer spillover in terms of a particular (dynamic) interconnection of the subsystems is thoroughly analyzed for in-domain and boundary control as well as sensing. This leads to the application of a small-gain theorem for interconnected systems based on input-to-output stability and unbounded observability properties. Moreover, an approach is presented for the computation of the required dimension of the slow subsystem used for controller design. Simulation scenarios for both scalar and coupled linear diffusion-reaction systems are used to underline the theoretical assessment and to give insight into the resulting properties of the interconnected systems.

Further data

Item Type: Preprint, postprint
Refereed: Yes
Keywords: Output stabilization; small-gain theory; diffusion-reaction systems; spillover; observer design; input-to-output stability; distributed parameter systems; partial differential equations; modal approximation
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Applied Mathematics
Profile Fields
Profile Fields > Advanced Fields
Profile Fields > Advanced Fields > Nonlinear Dynamics
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 19 Apr 2021 11:56
Last Modified: 19 Apr 2021 11:56
URI: https://eref.uni-bayreuth.de/id/eprint/64815