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

TL;DR

This paper presents a novel observer design method for coupled semilinear wave PDE systems, ensuring stability and disturbance attenuation, with validation through numerical simulation.

Contribution

It introduces a new approach for designing unknown input observers for coupled wave PDEs, including stability analysis and $H_{ abla}$ performance criteria.

Findings

Derived sufficient conditions for asymptotic stability

Established $H_{ abla}$ disturbance attenuation levels

Validated effectiveness through numerical simulation

Abstract

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 $H_{\infty}$ 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.