| 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. |
| 关键词: 1-D coupled wave network · Partial differential coupled system · Boundary delay · Controller design · Exponential stability |
| DOI：https://doi.org/10.1007/s11768-025-00256-8 |
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| 基金项目:This work was supported by the National Natural Science Foundation of China (No. 12301579) and the Fundamental Research Funds for the Central Universities of Civil Aviation University of China (No. 3122019140). |
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| Exponential stabilization of 1-D wave network with boundary delay |
| Yaru Xie1,Ruiqing Gao1 |
| (1 Department of Mathematics, Civil Aviation University of China, Tianjin 300300, China) |
| Abstract: |
| 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. |
| Key words: 1-D coupled wave network · Partial differential coupled system · Boundary delay · Controller design · Exponential stability |
