Stabilization of a Coupled Second Order ODE-wave System

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.

Citation

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.

Source Title

Proceedings of the 35th Chinese Control Conference

DOI

10.1109/ChiCC.2016.7553282

ISSN

1934-1768

School

Department of Mathematics and Statistics

Remarks

© 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

URI

http://hdl.handle.net/20.500.11937/40093

Collection

Curtin Research Publications