Stability and stabilization of infinite-dimensional linear port-Hamiltonian systems

Björn Augner; Birgit Jacob

doi:10.3934/eect.2014.3.207

Article Contents

2014, Volume 3, Issue 2: 207-229. Doi: 10.3934/eect.2014.3.207

This issue Previous Article Next Article On controllability of a linear elastic beam with memory under longitudinal load

Stability and stabilization of infinite-dimensional linear port-Hamiltonian systems

Björn Augner^1, and
Birgit Jacob^1,

1.
Fachbereich C - Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, Gaußstraße 20, D-42119 Wuppertal

Received: November 30, 2013

Revised: March 31, 2014

Published: May 2014

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Abstract

Stability and stabilization of linear port-Hamiltonian systems on infinite-dimensional spaces are investigated. This class is general enough to include models of beams and waves as well as transport and Schrödinger equations with boundary control and observation. The analysis is based on the frequency domain method which gives new results for second order port-Hamiltonian systems and hybrid systems. Stabilizing SIP or SOP controllers are designed. The obtained results are applied to the Euler-Bernoulli beam.

Keywords:

Infinite-dimensional linear port-Hamiltonian systems,
hybrid systems,
asymptotic stability,
exponential stability,
stabilization,
$C_0$-semigroup,
frequency domain method.

Mathematics Subject Classification: Primary: 93D15, 93D20; Secondary: 35L25, 47D06.

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