一类 2$\times$2 双曲偏微分系统的 PDP 边界控制

Abstract

Abstract:

This paper studies the exponential stability of a single open-channel system with constant slope and bottom friction, which is described by a $2\times2$ hyperbolic partial differential equation. The position feedback and delayed position feedback (PDP for short) boundary controller is designed to solve the problem of feedback stabilization. Firstly, the well-posedness of the system is proved by using operator semigroup theory. Then, the exponential stability of the closed-loop system is analyzed by constructing an appropriate Lyapunov function, and sufficient conditions for feedback parameters and time-delay are obtained. In addition, the asymptotic expressions of the eigenvalues and the eigenfunctions of the system operator are given by spectral analysis method. Finally, a numerical example is used to evaluate the performance of the PDP controller.

Key words: Hyperbolic PDE system, Lyapunov function, PDP boundary controller, Exponential stability

CLC Number:

O231.4

Pang Yuting,Zhao Dongxia,Zhao Xin,Gao Caixia. The PDP Boundary Control for a Class of 2$\times$2 Hyperbolic Partial Differential System[J].Acta mathematica scientia,Series A, 2023, 43(5): 1471-1482.

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The PDP Boundary Control for a Class of 2$\times$2 Hyperbolic Partial Differential System

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