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Dynamic polynomial stabilization of a 1D wave equation

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Details

Original languageEnglish
Title of host publication2019 Proceedings of the Conference on Control and its Applications
EditorsWilliam S. Levine, Richard Stockbridge
PublisherSIAM, Society for Industrial and Applied Mathematics
Pages105-109
Number of pages5
ISBN (Electronic)978-1-61197-575-8
DOIs
Publication statusPublished - 2019
Publication typeA4 Article in a conference publication
EventSIAM Conference on Control and its Applications - Chengdu, China
Duration: 19 Jun 201921 Jun 2019

Conference

ConferenceSIAM Conference on Control and its Applications
CountryChina
CityChengdu
Period19/06/1921/06/19

Abstract

We study observer-based dynamic stabilization of a one-dimensional wave equation with boundary control and distributed observation. The control system we consider is exponentially stabilizable but not exponentially detectable. Consequently, exponential energy decay is not achievable with dynamic output feedback. As our main result we design an observer-based controller which achieves rational decay of energy for a class of initial conditions. The controller design relies on helpful results on polynomial stability of semigroups generated by block operator matrices.

Publication forum classification

Field of science, Statistics Finland