Approximate observability and observer design for a wave equation with a quadratic-cubic nonlinear boundary condition
Abstract
This paper focuses on the approximate observability and observer design for a wave equation with a quadratic-cubic nonlinear boundary condition. First, the well-posedness of the wave equation is analysed by means of the method of characteristics and nonlinear boundary reflections. Subsequently, the approximate observability of the wave equation equipped with a boundary displacement output measurement is established. A state observer based on the same boundary displacement output measurement is then designed, and a sufficient condition that ensures the exponential stability of the estimation error system is provided. Rigorous theoretical proofs are presented for the well-posedness, approximate observability, and exponential stability of the estimation error system. Finally, numerical simulations are carried out to verify the effectiveness of the proposed observer.
Fields of Study & Subjects
Stability and Controllability of Differential Equations
Stability and Control of Uncertain Systems
Nonlinear Differential Equations Analysis
Publication details
- Journal / source
- International Journal of Control
- Publisher
- Informa UK Limited
- Volume
- 99
- Issue
- 7
- Pages
- 2016–2027
- Publication date
- 16 February 2026
- Language
- EN