Output feedback stabilization of a first‐order hyperbolic equation with multi‐point nonlocal term. Issue 4 (5th May 2021) - Hu, Qing‐Qing; Jin, Feng‐Fei; Yan, Baoqiang
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.