2025/10/06 by Patricio Guzmán, Guzmán, Patricio, Huerta, Agustín +2
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Electrical engineering #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2510.04893
openalex publication_date 2025/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study the rapid stabilization of an unstable wave equation, in which an unknown disturbance is located at the boundary condition. We address two different boundary conditions: Dirichlet- Dirichlet and Dirichlet-Neumann. In both cases, we design a feedback law, located at the same place as the unknown disturbance, that forces the exponential decay of the energy for any desired decay rate while suppressing the effects of the unknown disturbance. For the feedback design, we employ the backstepping method, Lyapunov techniques and the sign multivalued operator. The well-posedness of the closed-loop system, which is a differential inclusion, is shown with the maximal monotone operator theory.