Stabilization for a Cascaded ODE-Wave Equation with Boundary Nonlinear Disturbances
Abstract
In this article, we investigate the problem of exponential stabilization via output feedback for a cascaded system composed of an ordinary differential equation (ODE) and a wave partial differential equation (PDE) under boundary control. Four types of boundary interconnections are considered. In the absence of disturbances, a novel transformation is introduced to incorporate the PDE boundary control input into the ODE subsystem. Based on this transformation, a state feedback controller is designed to achieve exponential stability for both the ODE and PDE components. When internal uncertainties and external disturbances that match the control structure are present, a disturbance estimator is constructed. Utilizing this estimator, a Luenberger-type state observer is developed to reject the disturbances and exponentially stabilize the original system via an observer-based control scheme. Furthermore, the boundedness of the entire closed-loop system is rigorously established. Numerical simulations are provided to illustrate the theoretical results.
Cite
@article{arxiv.2605.10037,
title = {Stabilization for a Cascaded ODE-Wave Equation with Boundary Nonlinear Disturbances},
author = {Zhan-Dong Mei and Lan-Xi Tang},
journal= {arXiv preprint arXiv:2605.10037},
year = {2026}
}