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      Robust stabilization of the wave equation against small delays

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      Author
      Morgül, Ömer
      Date
      1994
      Source Title
      Proceedings of the 33rd IEEE Conference on Decision and Control, IEEE 1994
      Print ISSN
      0191-2216
      Publisher
      IEEE
      Pages
      1751 - 1756
      Language
      English
      Type
      Conference Paper
      Item Usage Stats
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      Abstract
      In this paper we consider a system which can be modeled by (undamped) wave equation in a bounded domain. We assume that the system is fixed at one end and is controlled by a boundary controller at the other end. We also considered two damped versions of this system, both parameterized by a nonnegative damping constant. We study two problems for these models, namely the stabilization by means of a boundary controller, and the stability robustness of the closed-loop system against small time delays in the feedback loop. We propose a class of finite dimensional dynamic boundary controllers to solve these problems. One basic feature of these controllers is that the corresponding controller transfer functions are required to be strictly positive real functions. We show that these controllers stabilize both damped and undamped models and solve the stability robustness problem for the damped models. It is also shown that while strict positive realness of the controller transfer functions is important for closed-loop stability, the strict properness is important for the stability robustness against small time delays in the feedback loop.
      Keywords
      Closed loop control systems
      Feedback control
      Mathematical models
      Parameter estimation
      Robustness (control systems)
      Transfer functions
      Boundary controllers
      Wave equation
      System stability
      Permalink
      http://hdl.handle.net/11693/27783
      Published Version (Please cite this version)
      https://doi.org/10.1109/CDC.1994.411182
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      • Department of Electrical and Electronics Engineering 3524
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