Output feedback stabilization of a first-order hyperbolic equation with multi-point nonlocal term

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.

Automated summary

The paper introduces the output feedback stabilization of a first-order hyperbolic equation with multi-point nonlocal term by boundary control. A boundary state feedback controller is designed using the backstepping method, ensuring exponential stability and constructing output feedback control based on an infinite-dimensional observer. The resulting closed-loop system is proven to be exponentially stable using operator semigroup theory, and the validity of the proposed controller is demonstrated through numerical simulations.