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Stabilization of a Coupled Second Order ODE-wave System

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Open access
Authors
Zhen, Z.
Wang, K.
Zhou, Z.
Loxton, Ryan
Date
2016
Type
Conference Paper

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Zhen, Z. and Wang, K. and Zhou, Z. and Loxton, R. 2016. Stabilization of a Coupled Second Order ODE-wave System, in Proceedings of the 35th Chinese Control Conference, 27-29 July 2016: IEEE.
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Proceedings of the 35th Chinese Control Conference
Source Conference
Proceedings of the 35th Chinese Control Conference
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Department of Mathematics and Statistics
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Abstract

This paper considers the stabilization of a coupled second order ODE-wave system, where the ODE dynamics contain the solution of the wave equation at an intermediate point. We design a stabilizing feedback controller by choosing a suitable target system and backstepping transformation. The backstepping transformation is defined in terms of several kernel functions, for which we establish existence, uniqueness and smoothness properties. We also prove exponential stability for the resulting closed-loop system. Finally, the effectiveness of the proposed feedback controller is verified via a numerical example.