Output feedback stabilization of a first‐order hyperbolic equation with multi‐point nonlocal term. Issue 4 (5th May 2021)

• Record Type: Journal Article
• Authors: Hu, Qing‐Qing; Jin, Feng‐Fei; Yan, Baoqiang
• Is Part Of: Asian journal of control. Volume 24:Issue 4(2022)
• Page Start: 1895
• Page End: 1903
• Publication Date: 2021-05-05
• Subjects: backstepping method -- first‐order hyperbolic equation -- multi‐point nonlocal term -- output feedback; Automatic control -- Periodicals; Control theory -- Periodicals; 629.805
• DOI: 10.1002/asjc.2583
• Languages: English
• ISSNs: 1561-8625

Abstract

Abstract: This paper presents the output feedback stabilization of a first‐order hyperbolic equation with multi‐point nonlocal term by boundary control. First of all, we utilize the backstepping method to design a boundary state feedback controller. On the basis of equivalence of original and target system, we guarantee the exponential stability of closed‐loop system. Hereafter, the output feedback control in the light of an infinite‐dimensional observer is constructed. We demonstrate that the resulting closed‐loop system is exponentially stable via operator semigroup theory. Finally, we display the validity of the proposed controller by some numerical simulations.