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Smyshlyaev, A., Cerpa, E. and Krstic, M. (2010) Boundary Stabilization of a 1-D Wave Equation with In-Domain Anti-Damping. SIAM Journal on Control and Optimization, 48, 4014-4031.
https://doi.org/10.1137/080742646

has been cited by the following article:

• TITLE: Output Feedback Regulation for 1-D Anti-Stable Wave Equation with External System Disturbance

  AUTHORS: Zhiyuan Li

  KEYWORDS: Anti-Stable Wave Equation, Distributed Disturbance, Exosystem, Output Feedback Regulation

  JOURNAL NAME: Engineering, Vol.12 No.9, September 22, 2020

  ABSTRACT: This paper has studied the output feedback regulation problem for 1-D anti-stable wave equation with distributed disturbance and a given reference signal generated by a finite-dimensional exosystem. We first design an observer for both exosystem and auxiliary PDE system to recover the state. Then we show the well-posedness of the regulator equations and propose an observer-based feedback control law to regulate the tracking error to zero exponentially and keep all the states bounded.