Asymptotic stabilization for a wave equation with periodic disturbance. (28th November 2019)

• Record Type: Journal Article
• Authors: Wei, Jing; Feng, Hongyinping; Guo, Bao-Zhu
• Is Part Of: IMA journal of mathematical control and information. Volume 37:Number 3(2020)
• Page Start: 894
• Page End: 917
• Publication Date: 2019-11-28
• Subjects: stability -- periodic disturbance -- coupled system; Control theory -- Periodicals; 629.831205
• DOI: 10.1093/imamci/dnz034
• Languages: English
• ISSNs: 0265-0754

Abstract

Abstract: In this paper, we consider boundary stabilization for a one-dimensional wave equation subject to periodic disturbance. By regarding the periodic signal as a boundary output of a free wave equation, we transform the controlled plant into a coupled wave system. We first design a state observer for the coupled system to estimate the disturbance and the system state simultaneously. An output feedback control is then designed to stabilize the original system. As an application, the result is applied to the stabilization of a wave equation with periodic disturbance suffering in output. Finally, some simulations are presented to validate the theoretical results.