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Output-feedback stabilization of an unstable wave equation
Krstic, Miroslav1; Guo, Bao-Zhu2,3; Balogh, Andras4; Smyshlyaev, Andrey1
Source PublicationAUTOMATICA
AbstractWe consider the problem of stabilization of a one-dimensional wave equation that contains instability at its free end and control on the opposite end. In contrast to classical collocated "boundary damper" feedbacks for the neutrally stable wave equations with one end satisfying a homogeneous boundary condition, the controllers and the associated observers designed in the paper are more complex due to the open-loop instability of the plant. The controller and observer gains are designed using the method of "backstepping," which results in explicit formulae for the gain functions. We prove exponential stability and the existence and uniqueness of classical solutions for the closed-loop system. We also derive the explicit compensators in frequency domain. The results are illustrated with simulations. (C) 2007 Elsevier Ltd. All rights reserved.
Keyworddistributed parameter systems wave equation backstepping stabilization boundary control
WOS Research AreaAutomation & Control Systems ; Engineering
WOS SubjectAutomation & Control Systems ; Engineering, Electrical & Electronic
WOS IDWOS:000253344000006
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Document Type期刊论文
Corresponding AuthorKrstic, Miroslav
Affiliation1.Univ Calif San Diego, Dept Mech & Aerosp Engn, La Jolla, CA 92093 USA
2.Acad Sinica, Acad Math & Syst Sci, Inst Syst Sci, Beijing 100080, Peoples R China
3.Univ Witwatersrand, Sch Computat & Appl Math, ZA-2050 Johannesburg, South Africa
4.Univ Texas Pan Amer, Dept Math, Edinburg, TX 78541 USA
Recommended Citation
GB/T 7714
Krstic, Miroslav,Guo, Bao-Zhu,Balogh, Andras,et al. Output-feedback stabilization of an unstable wave equation[J]. AUTOMATICA,2008,44(1):63-74.
APA Krstic, Miroslav,Guo, Bao-Zhu,Balogh, Andras,&Smyshlyaev, Andrey.(2008).Output-feedback stabilization of an unstable wave equation.AUTOMATICA,44(1),63-74.
MLA Krstic, Miroslav,et al."Output-feedback stabilization of an unstable wave equation".AUTOMATICA 44.1(2008):63-74.
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