Unknown input observer design for a class of coupled wave PDE systems

This paper deals with the problem of designing unknown input observers for a class of coupled semilinear wave partial differential equations (PDE) systems. A state observer is designed to estimate the uncertain coupled wave PDE systems. Then, the analysis of the asymptotic stability and $H_{\mathrm{\infty }}$ performance for the observer design of coupled wave PDE systems is investigated. Some sufficient conditions of asymptotic stability for the observer error system with disturbance attenuation level are derived via matrix inequalities based on the Lyapunov stability theory. Finally, a numerical simulation is presented to demonstrate the effectiveness of the obtained result.