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Output Feedback Stabilization for an ODE Coupled with a Wave Equation with Variable Coefficients

机译:Output Feedback Stabilization for an ODE Coupled with a Wave Equation with Variable Coefficients

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摘要

In this paper, we are concerned with the output feedback problem for coupled ODE-wave systems subject to spatially-varying coefficients. An original transformation is designed to turn the wave equation into an equation of the same type with constant coefficient and low order term. Taking advantage of the backstepping method, a state observer is constructed by non-collocated boundary displacement and velocity measurement. Output feedback on the based of the observer output feedback is then constructed, which makes use of the backstepping method to make the system exponentially stable. Finally, we demonstrate the well-posed and the exponential stability of the closed-loop system.

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