Brief paper: The strong stabilization of a one-dimensional wave equation by non-collocated dynamic boundary feedback control

Authors:
Bao-Zhu Guo;Wei Guo
Affiliations:
School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa and Academy of Mathematics and Systems Science, Academia Sini ...;School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa and School of Information Technology and Management, Universi ...
Venue:
Automatica (Journal of IFAC)
Year:
2009

Citing 4
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Abstract

The stabilization of a one-dimensional wave equation with non-collocated observation at its unstable free end and control at another end is considered. The controller comprises a state estimator which is designed in the case where the velocity is not available. The method of ''backstepping'' is adopted in our design of the feedback law. We use the theory of C"0-semigroups and Lyapunov functionals to prove the strong stability of the resulting closed-loop system.