Stabilizing Schrödinger—ODE systems with boundary delay for industrial process optimization

Ya-Ru Xie; Yu-Wen Chen; Cong-Yue Tian; Rui-Qing Gao; Li Zhang

doi:10.59400/adecp2712

Stabilizing Schrödinger—ODE systems with boundary delay for industrial process optimization

Ya-Ru Xie Mathematics, Civil Aviation University of China, Tianjin 300300, China
Yu-Wen Chen Mathematics, Civil Aviation University of China, Tianjin 300300, China
Cong-Yue Tian Mathematics, Civil Aviation University of China, Tianjin 300300, China
Rui-Qing Gao School of Science, Tianjin University of Commerce, Tianjin 300134, China
Li Zhang Mathematics, Civil Aviation University of China, Tianjin 300300, China

Article ID: 2712

DOI: https://doi.org/10.59400/adecp2712

Keywords: Schrödinger-ODE cascaded systems; exponential stability; integral-type feedback control; kernel function

Abstract

In this paper, we focus on the stabilization of a Schrödinger-ODE cascaded system with boundary delayed control. The system is stabilized through the utilization of integral-type feedback control, in which the integral kernel functions serve as parameters. The objective is to identify an appropriate set of kernel functions that ensure exponential stability characteristics of the closed-loop system. The initial step is to select a target system that must be exponentially stable. We propose an auxiliary system for the task at hand. Initially, we need to establish the equivalence between the auxiliary system and the original controlled time-delay system. This stage is primarily concerned with the elimination of the influence of input memory. The second system is leveraged to ascertain the equivalence between stable target system and the auxiliary system. This paper presents a method to choose parameter functions to create an exponentially stable feedback controller.

Published

2025-04-24

How to Cite

Xie, Y.-R., Chen, Y.-W., Tian, C.-Y., Gao, R.-Q., & Zhang, L. (2025). Stabilizing Schrödinger—ODE systems with boundary delay for industrial process optimization. Advances in Differential Equations and Control Processes, 32(2), 2712. https://doi.org/10.59400/adecp2712

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Vol. 32 No. 2 (2025)

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Article

This work is licensed under a Creative Commons Attribution 4.0 International License.

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