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<p>In this paper, we delve into the problem of exponential stability for a coupled system of a one-dimensional (1-D) N-root wave network with boundary delays. Our aim is to establish a universal controller design strategy, where the designed controller must guarantee the stability of the closed-loop system. The research approach undertaken in this paper assumes that the system state is known. We employ an integral-type feedback controller to achieve system stability, where the integral kernel function serves as a parameter. We attempt to select the corresponding exponentially stable system as the target system, and then construct a bounded linear transformation to demonstrate the equivalence between the target system and the original system, thereby eliminating the adverse effects of time delays on the system. The crux lies in determining the equation that the kernel function must satisfy. Herein, we primarily present a methodology for selecting the parameter function within this transformation, to achieve an exponentially stable feedback controller.</p>

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Exponential stabilization of 1-D wave network with boundary delay

  • 期刊论文

  • 发表日期：

    2025年5月21日

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  • Yaru Xie,
  • Ruiqing Gao

摘要

In this paper, we delve into the problem of exponential stability for a coupled system of a one-dimensional (1-D) N-root wave network with boundary delays. Our aim is to establish a universal controller design strategy, where the designed controller must guarantee the stability of the closed-loop system. The research approach undertaken in this paper assumes that the system state is known. We employ an integral-type feedback controller to achieve system stability, where the integral kernel function serves as a parameter. We attempt to select the corresponding exponentially stable system as the target system, and then construct a bounded linear transformation to demonstrate the equivalence between the target system and the original system, thereby eliminating the adverse effects of time delays on the system. The crux lies in determining the equation that the kernel function must satisfy. Herein, we primarily present a methodology for selecting the parameter function within this transformation, to achieve an exponentially stable feedback controller.