2025/01/27 by Florent Koudohode, Koudohode, Florent, Nikolaos Bekiaris‐Liberis +1
Computer Science · #Analysis of PDEs (math.AP) #FOS: Electrical engineering #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2501.15924
openalex publication_date 2025/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.