Stabilization of an unstable reaction-diffusion PDE with input delay despite state and input quantization

Florent Koudohode; Nikolaos Bekiaris-Liberis

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arXiv · 2501.15924

Stabilization of an unstable reaction-diffusion PDE with input delay despite state and input quantization

Florent Koudohode·Nikolaos Bekiaris-Liberis

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Abstract

We solve the global asymptotic stability problem of an unstable reaction-diffusion Partial Differential Equation (PDE) subject to input delay and state quantization developing a switched predictor-feedback law. To deal with the input delay, we reformulate the problem as an actuated transport PDE coupled with the original reaction-diffusion PDE. Then, we design a quantized predictor-based feedback mechanism that employs a dynamic switching strategy to adjust the quantization range and error over time. The stability of the closed-loop system is proven properly combining backstepping with a small-gain approach and input-to-state stability techniques, for deriving estimates on solutions, despite the quantization effect and the system's instability. We also extend this result to the input quantization case.

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Florent Koudohode, Nikolaos Bekiaris-Liberis. 2025-01-27. Stabilization of an unstable reaction-diffusion PDE with input delay despite state and input quantization. https://arxiv.org/abs/2501.15924

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